Chapter 1 SEM Analyses
Michael Roy
Thank you everyone for all of your feedback! Basically, what I’m looking for is what you guys think about these models. Are they clear? Did I mess anything? What conclusions would you draw from each one? What is important? What can I remove? Are there models that I missed? General thoughts?
I’m going to go through each model in detail tomorrow, so don’t worry about trying to piece everything together if things aren’t clear!
Name Key Information
Combined_Data_Full Name Key
Year = Year (Character, 2017 and 2018)
Location: NAN = Nantucket, PIE = Plum Island Estuary
Cage_Num = The First Number is the Replication, and the Second Number is the Initial Fiddler Crab Densities Which Includes 0, 4, 8, 12, 16, and 20, so 1_4 is Replication 1, 4 crab treatment
Replication = Replication (there are four replications per site per year)
Density_NN = the initial crab density treatment
Density_Num = the number of crabs placed in each plot
Pre_Live_SD = Initial Live Spartina alterniflora density before the experiment started (Spartina Density, SD)
Pre_Dead_SD = Initial Dead Spartina alterniflora density before the experiment started (Spartina Density, SD)
Pre_Pene_1, Pre_Pene_2, Pre_Pene_3 = the three soil strength measurements at the beginning of the experiment taken at the top left corner, the bottom left corner, and the bottom right corner, respectively (facing the creek)
Pre_Pene_AVG = The average initial soil strength taken from each of the three measurments for the plot
Post_Live_SD = Final Live Spartina alterniflora density at the end of the experiment (Spartina Density, SD)
Post_Dead_SD = Final Dead Spartina alterniflora density at the end of the experiment (Spartina Density, SD)
Post_Pene_1, Post_Pene_2, Post_Pene_3 = the three soil strength measurements at the end of the experiment taken at the top left corner, the bottom left corner, and the bottom right corner, respectively (facing the creek)
Post_Pene_AVG = The average final soil strength taken from each of the three measurments for the plot
Post_Burrow_Count = Burrow Density at the end of the Experiment
Spartina_Biomass = Dry biomass of Spartina alterniflora, clipped in the upper right corner of each plot
Site = The same as location, but as numeric and with 0s and 1s as locations, 0s are PIE, 1s are NAN
Year_Fac = The same as Year, but as numeric and with 0s and 1s as years, 0s are 2018, 1s are 2017 (don’t ask lol)
You can ignore the rest of the column names
Decomp_2018_3 Name Key
The names are the same for this object as Combined_Data_Full above with a couple of additions
Depth = The Depth in cm that the litter bags filled with Spartina alterniflora were buried
End_Mass_LB = The dry weight in g’s of what was left in the litter bags (I know it says lb, which was an oversight on my end, but it is what it is now lol)
Piecewise SEM for Soil Strength
Soil Strength Models
#### Building the Models - Final Soil Strength ####
## Final Soil Strength
Post_Pene_lm <- lm(data = combined_data_full,
Post_Pene_AVG ~
Post_Burrow_Count +
Pre_Pene_AVG +
Site +
Year_Fac
)
summary(Post_Pene_lm)##
## Call:
## lm(formula = Post_Pene_AVG ~ Post_Burrow_Count + Pre_Pene_AVG +
## Site + Year_Fac, data = combined_data_full)
##
## Residuals:
## Min 1Q Median 3Q Max
## -21.3622 -5.3154 0.4843 4.6029 22.8745
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 26.6496 3.1676 8.413 5.31e-13 ***
## Post_Burrow_Count -0.4129 0.1426 -2.895 0.00475 **
## Pre_Pene_AVG 0.3192 0.1169 2.729 0.00762 **
## Site -7.1675 2.9147 -2.459 0.01582 *
## Year_Fac -4.2785 1.9730 -2.169 0.03273 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 8.01 on 91 degrees of freedom
## Multiple R-squared: 0.5665, Adjusted R-squared: 0.5475
## F-statistic: 29.74 on 4 and 91 DF, p-value: 8.103e-16#Revised Names
Post_Pene_lm_2 <- lm(data = combined_data_full_2,
Final_Soil_Strength ~
Burrow_Density +
Initial_Soil_Strength +
Site +
Year
)
summary(Post_Pene_lm_2)##
## Call:
## lm(formula = Final_Soil_Strength ~ Burrow_Density + Initial_Soil_Strength +
## Site + Year, data = combined_data_full_2)
##
## Residuals:
## Min 1Q Median 3Q Max
## -21.3622 -5.3154 0.4843 4.6029 22.8745
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 26.6496 3.1676 8.413 5.31e-13 ***
## Burrow_Density -0.4129 0.1426 -2.895 0.00475 **
## Initial_Soil_Strength 0.3192 0.1169 2.729 0.00762 **
## Site -7.1675 2.9147 -2.459 0.01582 *
## Year -4.2785 1.9730 -2.169 0.03273 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 8.01 on 91 degrees of freedom
## Multiple R-squared: 0.5665, Adjusted R-squared: 0.5475
## F-statistic: 29.74 on 4 and 91 DF, p-value: 8.103e-16#Burrows
Burrows_NBglm <- glm.nb(data = combined_data_full,
Post_Burrow_Count ~
Density_Num *
Pre_Pene_AVG +
Site +
Year_Fac
,
link = "log"
)
summary(Burrows_NBglm)##
## Call:
## glm.nb(formula = Post_Burrow_Count ~ Density_Num * Pre_Pene_AVG +
## Site + Year_Fac, data = combined_data_full, link = "log",
## init.theta = 6.930012647)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -2.6041 -0.9683 -0.1138 0.4572 2.6459
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 0.9879996 0.2690349 3.672 0.00024 ***
## Density_Num -0.0085082 0.0136527 -0.623 0.53316
## Pre_Pene_AVG -0.0131145 0.0125118 -1.048 0.29456
## Site 1.9953157 0.1718184 11.613 < 2e-16 ***
## Year_Fac -0.7975175 0.1220847 -6.532 6.47e-11 ***
## Density_Num:Pre_Pene_AVG 0.0026698 0.0009478 2.817 0.00485 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for Negative Binomial(6.93) family taken to be 1)
##
## Null deviance: 415.55 on 95 degrees of freedom
## Residual deviance: 118.46 on 90 degrees of freedom
## AIC: 506.87
##
## Number of Fisher Scoring iterations: 1
##
##
## Theta: 6.93
## Std. Err.: 2.14
##
## 2 x log-likelihood: -492.875Burrows_NBglm_alt <- glm.nb(data = combined_data_full,
Post_Burrow_Count ~
Density_Num *
Pre_Pene_AVG *
Site +
Year_Fac
,
link = "log"
)
summary(Burrows_NBglm)##
## Call:
## glm.nb(formula = Post_Burrow_Count ~ Density_Num * Pre_Pene_AVG +
## Site + Year_Fac, data = combined_data_full, link = "log",
## init.theta = 6.930012647)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -2.6041 -0.9683 -0.1138 0.4572 2.6459
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 0.9879996 0.2690349 3.672 0.00024 ***
## Density_Num -0.0085082 0.0136527 -0.623 0.53316
## Pre_Pene_AVG -0.0131145 0.0125118 -1.048 0.29456
## Site 1.9953157 0.1718184 11.613 < 2e-16 ***
## Year_Fac -0.7975175 0.1220847 -6.532 6.47e-11 ***
## Density_Num:Pre_Pene_AVG 0.0026698 0.0009478 2.817 0.00485 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for Negative Binomial(6.93) family taken to be 1)
##
## Null deviance: 415.55 on 95 degrees of freedom
## Residual deviance: 118.46 on 90 degrees of freedom
## AIC: 506.87
##
## Number of Fisher Scoring iterations: 1
##
##
## Theta: 6.93
## Std. Err.: 2.14
##
## 2 x log-likelihood: -492.875#Let's compare a linear model to the NB
Burrows_lm <- lm(data = combined_data_full,
Post_Burrow_Count ~
Density_Num *
Pre_Pene_AVG +
Year_Fac +
Site
)
summary(Burrows_lm)##
## Call:
## lm(formula = Post_Burrow_Count ~ Density_Num * Pre_Pene_AVG +
## Year_Fac + Site, data = combined_data_full)
##
## Residuals:
## Min 1Q Median 3Q Max
## -13.3514 -3.4803 -0.8065 2.4255 18.6726
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 4.170912 2.649850 1.574 0.119
## Density_Num -0.048296 0.154579 -0.312 0.755
## Pre_Pene_AVG -0.007412 0.108794 -0.068 0.946
## Year_Fac -6.327155 1.273144 -4.970 3.18e-06 ***
## Site 13.651552 1.611037 8.474 4.27e-13 ***
## Density_Num:Pre_Pene_AVG 0.010659 0.008863 1.203 0.232
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 5.827 on 90 degrees of freedom
## Multiple R-squared: 0.6201, Adjusted R-squared: 0.599
## F-statistic: 29.38 on 5 and 90 DF, p-value: < 2.2e-16#Let's also throw in gamma for kicks
Burrows_glm <- glm(data = subset(combined_data_full, Post_Burrow_Count > 0),
Post_Burrow_Count ~
Density_Num *
Pre_Pene_AVG +
Year_Fac +
Site +
Mean_Burrows,
family = Gamma(link = "log")
)
summary(Burrows_glm)##
## Call:
## glm(formula = Post_Burrow_Count ~ Density_Num * Pre_Pene_AVG +
## Year_Fac + Site + Mean_Burrows, family = Gamma(link = "log"),
## data = subset(combined_data_full, Post_Burrow_Count > 0))
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -1.50474 -0.36493 -0.08467 0.20789 1.17274
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.9593009 0.2859883 3.354 0.00126 **
## Density_Num 0.0104094 0.0143070 0.728 0.46917
## Pre_Pene_AVG 0.0093490 0.0138044 0.677 0.50036
## Year_Fac -0.4242182 0.1991209 -2.130 0.03646 *
## Site 1.2680994 0.2628177 4.825 7.32e-06 ***
## Mean_Burrows 0.0306252 0.0197106 1.554 0.12451
## Density_Num:Pre_Pene_AVG 0.0006266 0.0010273 0.610 0.54380
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for Gamma family taken to be 0.2449195)
##
## Null deviance: 65.925 on 80 degrees of freedom
## Residual deviance: 20.017 on 74 degrees of freedom
## AIC: 449.34
##
## Number of Fisher Scoring iterations: 6#Pull the AIC and BIC values
AIC(Burrows_NBglm, Burrows_lm, Burrows_NBglm_alt)## df AIC
## Burrows_NBglm 7 506.8745
## Burrows_lm 7 618.6297
## Burrows_NBglm_alt 10 510.2402BIC(Burrows_NBglm, Burrows_lm, Burrows_NBglm_alt)## df BIC
## Burrows_NBglm 7 524.8250
## Burrows_lm 7 636.5801
## Burrows_NBglm_alt 10 535.8837#Revised Names
Burrows_NBglm_2 <- glm.nb(data = combined_data_full_2,
Burrow_Density ~
Crab_Density *
Initial_Soil_Strength +
Year +
Site
,
link = "log"
)
summary(Burrows_NBglm_2)##
## Call:
## glm.nb(formula = Burrow_Density ~ Crab_Density * Initial_Soil_Strength +
## Year + Site, data = combined_data_full_2, link = "log", init.theta = 6.930012647)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -2.6041 -0.9683 -0.1138 0.4572 2.6459
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 0.9879996 0.2690349 3.672 0.00024 ***
## Crab_Density -0.0085082 0.0136527 -0.623 0.53316
## Initial_Soil_Strength -0.0131145 0.0125118 -1.048 0.29456
## Year -0.7975175 0.1220847 -6.532 6.47e-11 ***
## Site 1.9953157 0.1718184 11.613 < 2e-16 ***
## Crab_Density:Initial_Soil_Strength 0.0026698 0.0009478 2.817 0.00485 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for Negative Binomial(6.93) family taken to be 1)
##
## Null deviance: 415.55 on 95 degrees of freedom
## Residual deviance: 118.46 on 90 degrees of freedom
## AIC: 506.87
##
## Number of Fisher Scoring iterations: 1
##
##
## Theta: 6.93
## Std. Err.: 2.14
##
## 2 x log-likelihood: -492.875#Initial Soil Strength
Pre_Pene_lm <- lm(data = combined_data_full,
Pre_Pene_AVG ~
Site +
Year_Fac
)
summary(Pre_Pene_lm)##
## Call:
## lm(formula = Pre_Pene_AVG ~ Site + Year_Fac, data = combined_data_full)
##
## Residuals:
## Min 1Q Median 3Q Max
## -15.3959 -4.8117 -0.7326 4.7732 18.6041
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 23.729 1.260 18.838 < 2e-16 ***
## Site -12.667 1.455 -8.709 1.1e-13 ***
## Year_Fac -5.334 1.455 -3.667 0.000409 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 7.126 on 93 degrees of freedom
## Multiple R-squared: 0.4898, Adjusted R-squared: 0.4788
## F-statistic: 44.64 on 2 and 93 DF, p-value: 2.566e-14summary(lm(data = combined_data_full,
Pre_Pene_AVG ~
Post_Burrow_Count +
Site +
Year
,
))##
## Call:
## lm(formula = Pre_Pene_AVG ~ Post_Burrow_Count + Site + Year,
## data = combined_data_full)
##
## Residuals:
## Min 1Q Median 3Q Max
## -15.679 -4.811 -0.955 4.624 18.518
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 18.48199 1.26721 14.585 < 2e-16 ***
## Post_Burrow_Count 0.09834 0.12674 0.776 0.43978
## Site -13.90025 2.15670 -6.445 5.23e-09 ***
## Year2018 4.66973 1.69014 2.763 0.00692 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 7.141 on 92 degrees of freedom
## Multiple R-squared: 0.4931, Adjusted R-squared: 0.4766
## F-statistic: 29.84 on 3 and 92 DF, p-value: 1.457e-13#Revised Names
Pre_Pene_lm_2 <- lm(data = combined_data_full_2,
Initial_Soil_Strength ~
Site +
Year
)
summary(Pre_Pene_lm_2)##
## Call:
## lm(formula = Initial_Soil_Strength ~ Site + Year, data = combined_data_full_2)
##
## Residuals:
## Min 1Q Median 3Q Max
## -15.3959 -4.8117 -0.7326 4.7732 18.6041
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 23.729 1.260 18.838 < 2e-16 ***
## Site -12.667 1.455 -8.709 1.1e-13 ***
## Year -5.334 1.455 -3.667 0.000409 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 7.126 on 93 degrees of freedom
## Multiple R-squared: 0.4898, Adjusted R-squared: 0.4788
## F-statistic: 44.64 on 2 and 93 DF, p-value: 2.566e-14#### Soil Strength Piecewise SEM ####
#Original Names
SS_Model <- psem(Burrows_NBglm,
Post_Pene_lm,
Pre_Pene_lm
)
summary(SS_Model)##
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## Structural Equation Model of SS_Model
##
## Call:
## Post_Burrow_Count ~ Density_Num * Pre_Pene_AVG + Site + Year_Fac
## Post_Pene_AVG ~ Post_Burrow_Count + Pre_Pene_AVG + Site + Year_Fac
## Pre_Pene_AVG ~ Site + Year_Fac
##
## AIC BIC
## 37.353 80.947
##
## ---
## Tests of directed separation:
##
## Independ.Claim Test.Type DF Crit.Value P.Value
## Pre_Pene_AVG ~ Density_Num + ... coef 92 -0.7572 0.4508
## Post_Pene_AVG ~ Density_Num + ... coef 90 -0.8192 0.4148
##
## Global goodness-of-fit:
##
## Fisher's C = 3.353 with P-value = 0.501 and on 4 degrees of freedom
##
## ---
## Coefficients:
##
## Response Predictor Estimate Std.Error DF Crit.Value
## Post_Burrow_Count Density_Num -0.0085 0.0137 90 -0.6232
## Post_Burrow_Count Pre_Pene_AVG -0.0131 0.0125 90 -1.0482
## Post_Burrow_Count Site 1.9953 0.1718 90 11.6129
## Post_Burrow_Count Year_Fac -0.7975 0.1221 90 -6.5325
## Post_Burrow_Count Density_Num:Pre_Pene_AVG 0.0027 0.0009 90 2.8167
## Post_Pene_AVG Post_Burrow_Count -0.4129 0.1426 91 -2.8949
## Post_Pene_AVG Pre_Pene_AVG 0.3192 0.1169 91 2.7295
## Post_Pene_AVG Site -7.1675 2.9147 91 -2.4591
## Post_Pene_AVG Year_Fac -4.2785 1.9730 91 -2.1685
## Pre_Pene_AVG Site -12.6669 1.4545 93 -8.7087
## Pre_Pene_AVG Year_Fac -5.3335 1.4545 93 -3.6669
## P.Value Std.Estimate
## 0.5332 -
## 0.2946 -
## 0.0000 - ***
## 0.0000 - ***
## 0.0049 - **
## 0.0047 -0.3191 **
## 0.0076 0.2646 **
## 0.0158 -0.3025 *
## 0.0327 -0.1806 *
## 0.0000 -0.645 ***
## 0.0004 -0.2716 ***
##
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05
##
## ---
## Individual R-squared:
##
## Response method R.squared
## Post_Burrow_Count nagelkerke 0.97
## Post_Pene_AVG none 0.57
## Pre_Pene_AVG none 0.49#Revised Names
SS_Model_2 <- psem(Burrows_NBglm_2,
Post_Pene_lm_2,
Pre_Pene_lm_2
)
summary(SS_Model_2)##
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## Structural Equation Model of SS_Model_2
##
## Call:
## Burrow_Density ~ Crab_Density * Initial_Soil_Strength + Year + Site
## Final_Soil_Strength ~ Burrow_Density + Initial_Soil_Strength + Site + Year
## Initial_Soil_Strength ~ Site + Year
##
## AIC BIC
## 37.353 80.947
##
## ---
## Tests of directed separation:
##
## Independ.Claim Test.Type DF Crit.Value P.Value
## Initial_Soil_Strength ~ Crab_Density + ... coef 92 -0.7572 0.4508
## Final_Soil_Strength ~ Crab_Density + ... coef 90 -0.8192 0.4148
##
## Global goodness-of-fit:
##
## Fisher's C = 3.353 with P-value = 0.501 and on 4 degrees of freedom
##
## ---
## Coefficients:
##
## Response Predictor Estimate Std.Error DF
## Burrow_Density Crab_Density -0.0085 0.0137 90
## Burrow_Density Initial_Soil_Strength -0.0131 0.0125 90
## Burrow_Density Year -0.7975 0.1221 90
## Burrow_Density Site 1.9953 0.1718 90
## Burrow_Density Crab_Density:Initial_Soil_Strength 0.0027 0.0009 90
## Final_Soil_Strength Burrow_Density -0.4129 0.1426 91
## Final_Soil_Strength Initial_Soil_Strength 0.3192 0.1169 91
## Final_Soil_Strength Site -7.1675 2.9147 91
## Final_Soil_Strength Year -4.2785 1.9730 91
## Initial_Soil_Strength Site -12.6669 1.4545 93
## Initial_Soil_Strength Year -5.3335 1.4545 93
## Crit.Value P.Value Std.Estimate
## -0.6232 0.5332 -
## -1.0482 0.2946 -
## -6.5325 0.0000 - ***
## 11.6129 0.0000 - ***
## 2.8167 0.0049 - **
## -2.8949 0.0047 -0.3191 **
## 2.7295 0.0076 0.2646 **
## -2.4591 0.0158 -0.3025 *
## -2.1685 0.0327 -0.1806 *
## -8.7087 0.0000 -0.645 ***
## -3.6669 0.0004 -0.2716 ***
##
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05
##
## ---
## Individual R-squared:
##
## Response method R.squared
## Burrow_Density nagelkerke 0.97
## Final_Soil_Strength none 0.57
## Initial_Soil_Strength none 0.49## NAN
#Final Soil Strength
Post_Pene_lm_NAN <- lm(data = fidd_NAN,
Post_Pene_AVG ~
Post_Burrow_Count +
Pre_Pene_AVG +
Year_Fac
)
summary(Post_Pene_lm_NAN)##
## Call:
## lm(formula = Post_Pene_AVG ~ Post_Burrow_Count + Pre_Pene_AVG +
## Year_Fac, data = fidd_NAN)
##
## Residuals:
## Min 1Q Median 3Q Max
## -13.559 -3.639 -0.136 3.942 11.917
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 18.2085 2.7581 6.602 4.39e-08 ***
## Post_Burrow_Count -0.1912 0.1229 -1.556 0.127
## Pre_Pene_AVG -0.1672 0.1347 -1.242 0.221
## Year_Fac -0.2323 2.1343 -0.109 0.914
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 5.754 on 44 degrees of freedom
## Multiple R-squared: 0.1492, Adjusted R-squared: 0.09116
## F-statistic: 2.571 on 3 and 44 DF, p-value: 0.06618#Burrows
Burrows_NBglm_NAN <- glm.nb(data = fidd_NAN,
Post_Burrow_Count ~
Density_Num *
Pre_Pene_AVG +
Year_Fac
,
link = "log"
)
summary(Burrows_NBglm_NAN)##
## Call:
## glm.nb(formula = Post_Burrow_Count ~ Density_Num * Pre_Pene_AVG +
## Year_Fac, data = fidd_NAN, link = "log", init.theta = 8.672265666)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -2.8550 -0.5637 -0.1556 0.5572 1.7420
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 2.7844318 0.2052125 13.569 < 2e-16 ***
## Density_Num 0.0024927 0.0147978 0.168 0.866
## Pre_Pene_AVG 0.0164366 0.0198567 0.828 0.408
## Year_Fac -0.7578080 0.1312603 -5.773 7.77e-09 ***
## Density_Num:Pre_Pene_AVG 0.0005889 0.0015560 0.378 0.705
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for Negative Binomial(8.6723) family taken to be 1)
##
## Null deviance: 96.060 on 47 degrees of freedom
## Residual deviance: 49.324 on 43 degrees of freedom
## AIC: 316.23
##
## Number of Fisher Scoring iterations: 1
##
##
## Theta: 8.67
## Std. Err.: 2.87
##
## 2 x log-likelihood: -304.229#Initial Soil Strength
Pre_Pene_lm_NAN <- lm(data = fidd_NAN,
Pre_Pene_AVG ~
Year_Fac
)
summary(Pre_Pene_lm_NAN)##
## Call:
## lm(formula = Pre_Pene_AVG ~ Year_Fac, data = fidd_NAN)
##
## Residuals:
## Min 1Q Median 3Q Max
## -9.750 -5.051 -1.792 4.449 13.958
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 9.750 1.348 7.235 4.05e-09 ***
## Year_Fac -2.708 1.906 -1.421 0.162
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 6.602 on 46 degrees of freedom
## Multiple R-squared: 0.04205, Adjusted R-squared: 0.02123
## F-statistic: 2.019 on 1 and 46 DF, p-value: 0.162#SEM
SS_Model_NAN <- psem(Burrows_NBglm_NAN,
Post_Pene_lm_NAN,
Pre_Pene_lm_NAN
)
summary(SS_Model_NAN)##
|
| | 0%
|
|=================================== | 50%
|
|======================================================================| 100%##
## Structural Equation Model of SS_Model_NAN
##
## Call:
## Post_Burrow_Count ~ Density_Num * Pre_Pene_AVG + Year_Fac
## Post_Pene_AVG ~ Post_Burrow_Count + Pre_Pene_AVG + Year_Fac
## Pre_Pene_AVG ~ Year_Fac
##
## AIC BIC
## 30.058 56.255
##
## ---
## Tests of directed separation:
##
## Independ.Claim Test.Type DF Crit.Value P.Value
## Pre_Pene_AVG ~ Density_Num + ... coef 45 0.4719 0.6393
## Post_Pene_AVG ~ Density_Num + ... coef 43 0.5889 0.5590
##
## Global goodness-of-fit:
##
## Fisher's C = 2.058 with P-value = 0.725 and on 4 degrees of freedom
##
## ---
## Coefficients:
##
## Response Predictor Estimate Std.Error DF Crit.Value
## Post_Burrow_Count Density_Num 0.0025 0.0148 43 0.1684
## Post_Burrow_Count Pre_Pene_AVG 0.0164 0.0199 43 0.8278
## Post_Burrow_Count Year_Fac -0.7578 0.1313 43 -5.7733
## Post_Burrow_Count Density_Num:Pre_Pene_AVG 0.0006 0.0016 43 0.3785
## Post_Pene_AVG Post_Burrow_Count -0.1912 0.1229 44 -1.5557
## Post_Pene_AVG Pre_Pene_AVG -0.1672 0.1347 44 -1.2419
## Post_Pene_AVG Year_Fac -0.2323 2.1343 44 -0.1088
## Pre_Pene_AVG Year_Fac -2.7083 1.9058 46 -1.4211
## P.Value Std.Estimate
## 0.8662 -
## 0.4078 -
## 0.0000 - ***
## 0.7051 -
## 0.1269 -0.2912
## 0.2208 -0.1849
## 0.9138 -0.0194
## 0.1620 -0.2051
##
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05
##
## ---
## Individual R-squared:
##
## Response method R.squared
## Post_Burrow_Count nagelkerke 0.72
## Post_Pene_AVG none 0.15
## Pre_Pene_AVG none 0.04plot(SS_Model_NAN, show = "Estimate")## PIE
#Final Soil Strength
Post_Pene_lm_PIE <- lm(data = fidd_PIE,
Post_Pene_AVG ~
Post_Burrow_Count +
Pre_Pene_AVG +
Year_Fac
)
summary(Post_Pene_lm_PIE)##
## Call:
## lm(formula = Post_Pene_AVG ~ Post_Burrow_Count + Pre_Pene_AVG +
## Year_Fac, data = fidd_PIE)
##
## Residuals:
## Min 1Q Median 3Q Max
## -18.7948 -4.7842 -0.5941 4.5640 19.8739
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 19.76134 5.31900 3.715 0.00057 ***
## Post_Burrow_Count 0.06107 0.57130 0.107 0.91536
## Pre_Pene_AVG 0.58380 0.17736 3.292 0.00197 **
## Year_Fac -4.01794 3.20686 -1.253 0.21685
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 8.941 on 44 degrees of freedom
## Multiple R-squared: 0.3378, Adjusted R-squared: 0.2927
## F-statistic: 7.483 on 3 and 44 DF, p-value: 0.0003751#Burrows
Burrows_NBglm_PIE <- glm.nb(data = fidd_PIE,
Post_Burrow_Count ~
Density_Num *
Pre_Pene_AVG +
Year_Fac
,
link = "log"
)
summary(Burrows_NBglm_PIE)##
## Call:
## glm.nb(formula = Post_Burrow_Count ~ Density_Num * Pre_Pene_AVG +
## Year_Fac, data = fidd_PIE, link = "log", init.theta = 2.563558483)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -2.4881 -1.0992 -0.0991 0.4727 2.1451
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 1.272735 0.823357 1.546 0.12216
## Density_Num 0.007381 0.070715 0.104 0.91687
## Pre_Pene_AVG -0.031832 0.033008 -0.964 0.33486
## Year_Fac -0.990792 0.319527 -3.101 0.00193 **
## Density_Num:Pre_Pene_AVG 0.002734 0.003196 0.856 0.39224
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for Negative Binomial(2.5636) family taken to be 1)
##
## Null deviance: 76.695 on 47 degrees of freedom
## Residual deviance: 55.167 on 43 degrees of freedom
## AIC: 194.84
##
## Number of Fisher Scoring iterations: 1
##
##
## Theta: 2.56
## Std. Err.: 1.24
##
## 2 x log-likelihood: -182.842#Initial Soil Strength
Pre_Pene_lm_PIE <- lm(data = fidd_PIE,
Pre_Pene_AVG ~
Year_Fac
)
summary(Pre_Pene_lm_PIE)##
## Call:
## lm(formula = Pre_Pene_AVG ~ Year_Fac, data = fidd_PIE)
##
## Residuals:
## Min 1Q Median 3Q Max
## -14.0833 -4.9299 -0.0627 5.0095 19.9167
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 25.042 1.520 16.472 < 2e-16 ***
## Year_Fac -7.959 2.150 -3.702 0.000571 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 7.448 on 46 degrees of freedom
## Multiple R-squared: 0.2295, Adjusted R-squared: 0.2128
## F-statistic: 13.7 on 1 and 46 DF, p-value: 0.0005713#SEM
SS_Model_PIE <- psem(Burrows_NBglm_PIE,
Post_Pene_lm_PIE,
Pre_Pene_lm_PIE
)
summary(SS_Model_PIE)##
|
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|
|=================================== | 50%
|
|======================================================================| 100%##
## Structural Equation Model of SS_Model_PIE
##
## Call:
## Post_Burrow_Count ~ Density_Num * Pre_Pene_AVG + Year_Fac
## Post_Pene_AVG ~ Post_Burrow_Count + Pre_Pene_AVG + Year_Fac
## Pre_Pene_AVG ~ Year_Fac
##
## AIC BIC
## 35.601 61.798
##
## ---
## Tests of directed separation:
##
## Independ.Claim Test.Type DF Crit.Value P.Value
## Pre_Pene_AVG ~ Density_Num + ... coef 45 -1.4668 0.1494
## Post_Pene_AVG ~ Density_Num + ... coef 43 -1.4669 0.1497
##
## Global goodness-of-fit:
##
## Fisher's C = 7.601 with P-value = 0.107 and on 4 degrees of freedom
##
## ---
## Coefficients:
##
## Response Predictor Estimate Std.Error DF Crit.Value
## Post_Burrow_Count Density_Num 0.0074 0.0707 43 0.1044
## Post_Burrow_Count Pre_Pene_AVG -0.0318 0.0330 43 -0.9644
## Post_Burrow_Count Year_Fac -0.9908 0.3195 43 -3.1008
## Post_Burrow_Count Density_Num:Pre_Pene_AVG 0.0027 0.0032 43 0.8556
## Post_Pene_AVG Post_Burrow_Count 0.0611 0.5713 44 0.1069
## Post_Pene_AVG Pre_Pene_AVG 0.5838 0.1774 44 3.2916
## Post_Pene_AVG Year_Fac -4.0179 3.2069 44 -1.2529
## Pre_Pene_AVG Year_Fac -7.9587 2.1500 46 -3.7018
## P.Value Std.Estimate
## 0.9169 -
## 0.3349 -
## 0.0019 - **
## 0.3922 -
## 0.9154 0.0145
## 0.0020 0.461 **
## 0.2169 -0.191
## 0.0006 -0.4791 ***
##
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05
##
## ---
## Individual R-squared:
##
## Response method R.squared
## Post_Burrow_Count nagelkerke 0.45
## Post_Pene_AVG none 0.34
## Pre_Pene_AVG none 0.23plot(SS_Model_PIE, show = "Estimate")Soil Strength DAGs
plot(SS_Model, show = "Estimate")plot(SS_Model_2, show = "Estimate")# DiagrammeR Plots
## Including Site and Year
grViz("digraph Soil_Strength {
# a 'graph' statement
graph [overlap = false,
fontsize = 14]
# several 'node' statements
# Exogenous Variables
node [shape = rectangle,
fontname = Helvetica,
width = 1.3,
fontcolor = darkslategray,
color = darkslategray,
nodesep = 1,
penwidth = 2]
Crab_Density [label = '@@1']
Site [label = '@@5']
Year [label = '@@6']
# Endogenous Variables
node [shape = rectangle,
fixedsize = true,
width = 1.8,
color = steelblue,
fontcolor = darkslategray,
penwidth = 2]
Burrow_Density [label = '@@3']
Initial_SS [label = '@@4', color = darkslategray]
Final_SS [label = '@@7']
# Interaction
node [shape = rectangle,
fixedsize = true,
width = 2,
height = 0.9,
color = steelblue,
fontcolor = darkslategray,
penwidth = 2]
CrabSoil_Intrctn [label = '@@2']
# several 'edge' statements
edge [color = grey, arrowhead = normal, arrowtail = dot, penwidth = 1, minlen = 3]
Initial_SS->Burrow_Density
Crab_Density->Burrow_Density
edge [color = DimGray, arrowhead = normal, penwidth = 5, minlen = 5]
Site->Burrow_Density
Year->Burrow_Density
Burrow_Density->Final_SS [color = steelblue]
Site->Initial_SS
Year->Initial_SS
Site->Final_SS
Year->Final_SS
Initial_SS->Final_SS
edge [color = steelblue, arrowhead = normal, penwidth = 5, minlen = 4]
CrabSoil_Intrctn->Burrow_Density
}
[1]: 'Crab Density'
[2]: 'Crab Density and\\nInitial Soil Strength\\nInteraction\\n'
[3]: 'Burrow Density'
[4]: 'Initial Soil Strength'
[5]: 'Site'
[6]: 'Year'
[7]: 'Final Soil Strength'
"
)## Excluding Site and Year
grViz("digraph Soil_Strength {
# a 'graph' statement
graph [overlap = false,
fontsize = 14,
ranksep = .25]
# several 'node' statements
# Exogenous Variables
node [shape = rectangle,
fontname = Helvetica,
width = 1.3,
fontcolor = darkslategray,
color = darkslategray,
nodesep = 1,
penwidth = 2]
Crab_Density [label = '@@1']
CrabSoil_Intrctn [label = '@@2', color = steelblue, height = 0.9]
Initial_SS [label = '@@4']
# Endogenous Variables
node [shape = rectangle,
fixedsize = true,
width = 1.8,
color = steelblue,
fontcolor = darkslategray,
penwidth = 2]
Burrow_Density [label = '@@3']
Final_SS [label = '@@5']
# several 'edge' statements
edge [color = grey, arrowhead = normal, minlen = 4, penwidth = 1]
Initial_SS->Burrow_Density [label = '-0.013']
Crab_Density->Burrow_Density [label = '-0.0085']
edge [color = DimGray, arrowhead = normal, minlen = 6, penwidth = 5]
CrabSoil_Intrctn->Burrow_Density [color = steelblue, label = '0.0027']
Burrow_Density->Final_SS [color = steelblue, label = '-0.41']
Initial_SS->Final_SS [label = '0.32']
}
[1]: 'Crab Density'
[2]: 'Crab Density and\\nInitial Soil Strength\\nInteraction\\n'
[3]: 'Burrow Density'
[4]: 'Initial Soil Strength'
[5]: 'Final Soil Strength'
"
)Soil Strength Visreg
#### Visreg Plot Comparison ####
#Initial Soil Strength to Final Burrow Density by Initial Crab Density
visreg(Burrows_NBglm,
"Pre_Pene_AVG",
scale = "response",
by = "Density_Num",
breaks = c(0, 4, 8, 12, 16, 20),
ylab = "Crab Burrow Density",
xlab = "Initial Soil Strength"
)
#Initial Crab Density to Final Burrow Density by Soil Strength
visreg(Burrows_NBglm,
"Density_Num",
scale = "response",
by = c("Pre_Pene_AVG"),
breaks = c(0, 10, 20, 30),
ylab = "Crab Burrow Density",
xlab = "Initial Crab Density"
#gg = TRUE
) #+
#theme_bw() #+
#aes(color = "Site")
#Initial Burrow Density to Final Burrow Density
visreg(Burrows_NBglm,
"Density_Num",
scale = "response",
#by = c("Pre_Pene_AVG"),
#breaks = c(0, 4, 8, 12, 16, 20),
ylab = "Crab Burrow Density",
xlab = "Initial Crab Density"
#gg = TRUE
) #+## Conditions used in construction of plot
## Pre_Pene_AVG: 15.165
## Site: 0.5
## Year_Fac: 0.5
#theme_bw() #+
#aes(color = "Site")
#Initial Burrow Density to Final Burrow Density by Site
visreg(Post_Pene_lm,
"Post_Burrow_Count",
#scale = "response",
by = "Site",
#breaks = c(0, 4, 8, 12, 16, 20),
ylab = "Final Soil Strength",
xlab = "Crab Burrow Density"
)
#Initial Burrow Density to Final Burrow Density by Initial Soil Strength
visreg(Post_Pene_lm,
"Post_Burrow_Count",
#scale = "response",
by = "Pre_Pene_AVG",
breaks = c(0, 10, 20, 30),
ylab = "Final Soil Strength",
xlab = "Crab Burrow Density"
)
#Initial Soil Strength to Final Soil Strength by Site
visreg(Post_Pene_lm,
"Pre_Pene_AVG",
#scale = "response",
by = "Site",
#breaks = c(0, 10, 20, 30),
ylab = "Final Soil Strength",
xlab = "Initial Soil Strength"
)
##Initial Soil Strength to Final Soil Strength by Burrows
visreg(Post_Pene_lm,
"Pre_Pene_AVG",
#scale = "response",
by = "Post_Burrow_Count",
breaks = c(0, 10, 20, 30),
ylab = "Final Soil Strength",
xlab = "Initial Soil Strength"
)
## Two and Three Dimensional Visreg models
# Initial Soil Strength and Crab Density to Final Burrow Density Interaction 3D model
visreg2d(Burrows_NBglm,
"Pre_Pene_AVG",
"Density_Num",
scale = "response",
by = "Density_Num",
breaks = c(0, 4, 8, 12, 16, 20),
#ylab = "Crab Burrow Density",
xlab = "Initial Soil Strength",
plot.type = "rgl"
)
# Initial Soil Strength and Crab Density to Final Burrow Density Interaction Heat Map
visreg2d(Burrows_NBglm,
x="Pre_Pene_AVG",
y="Density_Num",
scale = "response",
main = "Final Burrow Density",
#by = "Density_Num",
#breaks = c(0, 4, 8, 12, 16, 20),
ylab = "Initial Crab Density",
xlab = "Initial Soil Strength",
#plot.type = "rgl"
)
VRB_2 <- visreg2d(Burrows_NBglm,
x="Pre_Pene_AVG",
y="Density_Num",
scale = "response",
#type = "contrast",
main = "Final Burrow Density",
#by = "Density_Num",
#breaks = c(0, 4, 8, 12, 16, 20),
color = c("black", "white", "red"),
ylab = "Initial Crab Density",
xlab = "Initial Soil Strength"#,
#plot.type = "persp"#,
#nn = 5#,
#plot.type = "rgl"
)
VRB <- visreg2d(Burrows_NBglm,
x="Pre_Pene_AVG",
y="Density_Num"#,
#scale = "response",
#main = "Final Burrow Density"#,
#by = "Density_Num",
#breaks = c(0, 4, 8, 12, 16, 20),
#ylab = "Initial Crab Density",
#xlab = "Initial Soil Strength"#,
#plot.type = "rgl"
)
str(VRB)## List of 4
## $ x : num [1:99] 0 0.378 0.755 1.133 1.51 ...
## $ y : num [1:99] 0 0.204 0.408 0.612 0.816 ...
## $ z : num [1:99, 1:99] 1.59 1.58 1.58 1.57 1.57 ...
## $ meta:List of 5
## ..$ x : chr "Pre_Pene_AVG"
## ..$ y : chr "Density_Num"
## ..$ trans:function (x)
## ..$ class: chr [1:3] "negbin" "glm" "lm"
## ..$ cond :'data.frame': 1 obs. of 2 variables:
## .. ..$ Site : num 0.5
## .. ..$ Year_Fac: num 0.5
## - attr(*, "class")= chr "visreg2d"show(VRB)## $x
## [1] 0.000000 0.377551 0.755102 1.132653 1.510204 1.887755 2.265306
## [8] 2.642857 3.020408 3.397959 3.775510 4.153061 4.530612 4.908163
## [15] 5.285714 5.663265 6.040816 6.418367 6.795918 7.173469 7.551020
## [22] 7.928571 8.306122 8.683673 9.061224 9.438776 9.816327 10.193878
## [29] 10.571429 10.948980 11.326531 11.704082 12.081633 12.459184 12.836735
## [36] 13.214286 13.591837 13.969388 14.346939 14.724490 15.102041 15.479592
## [43] 15.857143 16.234694 16.612245 16.989796 17.367347 17.744898 18.122449
## [50] 18.500000 18.877551 19.255102 19.632653 20.010204 20.387755 20.765306
## [57] 21.142857 21.520408 21.897959 22.275510 22.653061 23.030612 23.408163
## [64] 23.785714 24.163265 24.540816 24.918367 25.295918 25.673469 26.051020
## [71] 26.428571 26.806122 27.183673 27.561224 27.938776 28.316327 28.693878
## [78] 29.071429 29.448980 29.826531 30.204082 30.581633 30.959184 31.336735
## [85] 31.714286 32.091837 32.469388 32.846939 33.224490 33.602041 33.979592
## [92] 34.357143 34.734694 35.112245 35.489796 35.867347 36.244898 36.622449
## [99] 37.000000
##
## $y
## [1] 0.0000000 0.2040816 0.4081633 0.6122449 0.8163265 1.0204082
## [7] 1.2244898 1.4285714 1.6326531 1.8367347 2.0408163 2.2448980
## [13] 2.4489796 2.6530612 2.8571429 3.0612245 3.2653061 3.4693878
## [19] 3.6734694 3.8775510 4.0816327 4.2857143 4.4897959 4.6938776
## [25] 4.8979592 5.1020408 5.3061224 5.5102041 5.7142857 5.9183673
## [31] 6.1224490 6.3265306 6.5306122 6.7346939 6.9387755 7.1428571
## [37] 7.3469388 7.5510204 7.7551020 7.9591837 8.1632653 8.3673469
## [43] 8.5714286 8.7755102 8.9795918 9.1836735 9.3877551 9.5918367
## [49] 9.7959184 10.0000000 10.2040816 10.4081633 10.6122449 10.8163265
## [55] 11.0204082 11.2244898 11.4285714 11.6326531 11.8367347 12.0408163
## [61] 12.2448980 12.4489796 12.6530612 12.8571429 13.0612245 13.2653061
## [67] 13.4693878 13.6734694 13.8775510 14.0816327 14.2857143 14.4897959
## [73] 14.6938776 14.8979592 15.1020408 15.3061224 15.5102041 15.7142857
## [79] 15.9183673 16.1224490 16.3265306 16.5306122 16.7346939 16.9387755
## [85] 17.1428571 17.3469388 17.5510204 17.7551020 17.9591837 18.1632653
## [91] 18.3673469 18.5714286 18.7755102 18.9795918 19.1836735 19.3877551
## [97] 19.5918367 19.7959184 20.0000000
##
## $z
## [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8]
## [1,] 1.586899 1.585162 1.583426 1.581690 1.579953 1.578217 1.576480 1.574744
## [2,] 1.581947 1.580417 1.578886 1.577355 1.575825 1.574294 1.572763 1.571233
## [3,] 1.576996 1.575671 1.574346 1.573021 1.571696 1.570371 1.569046 1.567721
## [4,] 1.572045 1.570925 1.569806 1.568687 1.567568 1.566448 1.565329 1.564210
## [5,] 1.567093 1.566180 1.565266 1.564353 1.563439 1.562525 1.561612 1.560698
## [6,] 1.562142 1.561434 1.560726 1.560018 1.559310 1.558603 1.557895 1.557187
## [7,] 1.557190 1.556688 1.556186 1.555684 1.555182 1.554680 1.554178 1.553676
## [8,] 1.552239 1.551943 1.551646 1.551350 1.551053 1.550757 1.550461 1.550164
## [9,] 1.547288 1.547197 1.547106 1.547016 1.546925 1.546834 1.546743 1.546653
## [10,] 1.542336 1.542451 1.542566 1.542681 1.542796 1.542911 1.543026 1.543141
## [11,] 1.537385 1.537706 1.538026 1.538347 1.538668 1.538989 1.539309 1.539630
## [12,] 1.532433 1.532960 1.533486 1.534013 1.534539 1.535066 1.535592 1.536119
## [13,] 1.527482 1.528214 1.528946 1.529679 1.530411 1.531143 1.531875 1.532607
## [14,] 1.522531 1.523469 1.524406 1.525344 1.526282 1.527220 1.528158 1.529096
## [15,] 1.517579 1.518723 1.519866 1.521010 1.522154 1.523297 1.524441 1.525584
## [16,] 1.512628 1.513977 1.515327 1.516676 1.518025 1.519374 1.520724 1.522073
## [17,] 1.507677 1.509232 1.510787 1.512342 1.513897 1.515452 1.517007 1.518562
## [18,] 1.502725 1.504486 1.506247 1.508007 1.509768 1.511529 1.513289 1.515050
## [19,] 1.497774 1.499740 1.501707 1.503673 1.505639 1.507606 1.509572 1.511539
## [20,] 1.492822 1.494995 1.497167 1.499339 1.501511 1.503683 1.505855 1.508027
## [21,] 1.487871 1.490249 1.492627 1.495005 1.497382 1.499760 1.502138 1.504516
## [22,] 1.482920 1.485503 1.488087 1.490670 1.493254 1.495837 1.498421 1.501005
## [23,] 1.477968 1.480758 1.483547 1.486336 1.489125 1.491915 1.494704 1.497493
## [24,] 1.473017 1.476012 1.479007 1.482002 1.484997 1.487992 1.490987 1.493982
## [25,] 1.468066 1.471266 1.474467 1.477668 1.480868 1.484069 1.487270 1.490470
## [26,] 1.463114 1.466521 1.469927 1.473333 1.476740 1.480146 1.483552 1.486959
## [27,] 1.458163 1.461775 1.465387 1.468999 1.472611 1.476223 1.479835 1.483447
## [28,] 1.453211 1.457029 1.460847 1.464665 1.468483 1.472300 1.476118 1.479936
## [29,] 1.448260 1.452284 1.456307 1.460331 1.464354 1.468378 1.472401 1.476425
## [30,] 1.443309 1.447538 1.451767 1.455996 1.460226 1.464455 1.468684 1.472913
## [31,] 1.438357 1.442792 1.447227 1.451662 1.456097 1.460532 1.464967 1.469402
## [32,] 1.433406 1.438047 1.442687 1.447328 1.451968 1.456609 1.461250 1.465890
## [33,] 1.428455 1.433301 1.438147 1.442994 1.447840 1.452686 1.457533 1.462379
## [34,] 1.423503 1.428555 1.433607 1.438659 1.443711 1.448763 1.453816 1.458868
## [35,] 1.418552 1.423810 1.429067 1.434325 1.439583 1.444841 1.450098 1.455356
## [36,] 1.413600 1.419064 1.424527 1.429991 1.435454 1.440918 1.446381 1.451845
## [37,] 1.408649 1.414318 1.419987 1.425657 1.431326 1.436995 1.442664 1.448333
## [38,] 1.403698 1.409573 1.415447 1.421322 1.427197 1.433072 1.438947 1.444822
## [39,] 1.398746 1.404827 1.410907 1.416988 1.423069 1.429149 1.435230 1.441311
## [40,] 1.393795 1.400081 1.406368 1.412654 1.418940 1.425227 1.431513 1.437799
## [41,] 1.388843 1.395336 1.401828 1.408320 1.414812 1.421304 1.427796 1.434288
## [42,] 1.383892 1.390590 1.397288 1.403985 1.410683 1.417381 1.424079 1.430776
## [43,] 1.378941 1.385844 1.392748 1.399651 1.406555 1.413458 1.420361 1.427265
## [44,] 1.373989 1.381099 1.388208 1.395317 1.402426 1.409535 1.416644 1.423754
## [45,] 1.369038 1.376353 1.383668 1.390983 1.398297 1.405612 1.412927 1.420242
## [46,] 1.364087 1.371607 1.379128 1.386648 1.394169 1.401690 1.409210 1.416731
## [47,] 1.359135 1.366862 1.374588 1.382314 1.390040 1.397767 1.405493 1.413219
## [48,] 1.354184 1.362116 1.370048 1.377980 1.385912 1.393844 1.401776 1.409708
## [49,] 1.349232 1.357370 1.365508 1.373646 1.381783 1.389921 1.398059 1.406197
## [50,] 1.344281 1.352625 1.360968 1.369311 1.377655 1.385998 1.394342 1.402685
## [51,] 1.339330 1.347879 1.356428 1.364977 1.373526 1.382075 1.390625 1.399174
## [52,] 1.334378 1.343133 1.351888 1.360643 1.369398 1.378153 1.386907 1.395662
## [53,] 1.329427 1.338388 1.347348 1.356309 1.365269 1.374230 1.383190 1.392151
## [54,] 1.324476 1.333642 1.342808 1.351974 1.361141 1.370307 1.379473 1.388639
## [55,] 1.319524 1.328896 1.338268 1.347640 1.357012 1.366384 1.375756 1.385128
## [56,] 1.314573 1.324150 1.333728 1.343306 1.352884 1.362461 1.372039 1.381617
## [57,] 1.309621 1.319405 1.329188 1.338972 1.348755 1.358538 1.368322 1.378105
## [58,] 1.304670 1.314659 1.324648 1.334637 1.344627 1.354616 1.364605 1.374594
## [59,] 1.299719 1.309913 1.320108 1.330303 1.340498 1.350693 1.360888 1.371082
## [60,] 1.294767 1.305168 1.315568 1.325969 1.336369 1.346770 1.357170 1.367571
## [61,] 1.289816 1.300422 1.311028 1.321635 1.332241 1.342847 1.353453 1.364060
## [62,] 1.284865 1.295676 1.306488 1.317300 1.328112 1.338924 1.349736 1.360548
## [63,] 1.279913 1.290931 1.301948 1.312966 1.323984 1.335001 1.346019 1.357037
## [64,] 1.274962 1.286185 1.297409 1.308632 1.319855 1.331079 1.342302 1.353525
## [65,] 1.270010 1.281439 1.292869 1.304298 1.315727 1.327156 1.338585 1.350014
## [66,] 1.265059 1.276694 1.288329 1.299963 1.311598 1.323233 1.334868 1.346503
## [67,] 1.260108 1.271948 1.283789 1.295629 1.307470 1.319310 1.331151 1.342991
## [68,] 1.255156 1.267202 1.279249 1.291295 1.303341 1.315387 1.327434 1.339480
## [69,] 1.250205 1.262457 1.274709 1.286961 1.299213 1.311465 1.323716 1.335968
## [70,] 1.245253 1.257711 1.270169 1.282626 1.295084 1.307542 1.319999 1.332457
## [71,] 1.240302 1.252965 1.265629 1.278292 1.290956 1.303619 1.316282 1.328946
## [72,] 1.235351 1.248220 1.261089 1.273958 1.286827 1.299696 1.312565 1.325434
## [73,] 1.230399 1.243474 1.256549 1.269624 1.282698 1.295773 1.308848 1.321923
## [74,] 1.225448 1.238728 1.252009 1.265289 1.278570 1.291850 1.305131 1.318411
## [75,] 1.220497 1.233983 1.247469 1.260955 1.274441 1.287928 1.301414 1.314900
## [76,] 1.215545 1.229237 1.242929 1.256621 1.270313 1.284005 1.297697 1.311389
## [77,] 1.210594 1.224491 1.238389 1.252287 1.266184 1.280082 1.293980 1.307877
## [78,] 1.205642 1.219746 1.233849 1.247952 1.262056 1.276159 1.290262 1.304366
## [79,] 1.200691 1.215000 1.229309 1.243618 1.257927 1.272236 1.286545 1.300854
## [80,] 1.195740 1.210254 1.224769 1.239284 1.253799 1.268313 1.282828 1.297343
## [81,] 1.190788 1.205509 1.220229 1.234950 1.249670 1.264391 1.279111 1.293831
## [82,] 1.185837 1.200763 1.215689 1.230615 1.245542 1.260468 1.275394 1.290320
## [83,] 1.180886 1.196017 1.211149 1.226281 1.241413 1.256545 1.271677 1.286809
## [84,] 1.175934 1.191272 1.206609 1.221947 1.237285 1.252622 1.267960 1.283297
## [85,] 1.170983 1.186526 1.202069 1.217613 1.233156 1.248699 1.264243 1.279786
## [86,] 1.166031 1.181780 1.197529 1.213278 1.229027 1.244776 1.260525 1.276274
## [87,] 1.161080 1.177035 1.192989 1.208944 1.224899 1.240854 1.256808 1.272763
## [88,] 1.156129 1.172289 1.188450 1.204610 1.220770 1.236931 1.253091 1.269252
## [89,] 1.151177 1.167543 1.183910 1.200276 1.216642 1.233008 1.249374 1.265740
## [90,] 1.146226 1.162798 1.179370 1.195941 1.212513 1.229085 1.245657 1.262229
## [91,] 1.141275 1.158052 1.174830 1.191607 1.208385 1.225162 1.241940 1.258717
## [92,] 1.136323 1.153306 1.170290 1.187273 1.204256 1.221239 1.238223 1.255206
## [93,] 1.131372 1.148561 1.165750 1.182939 1.200128 1.217317 1.234506 1.251695
## [94,] 1.126420 1.143815 1.161210 1.178604 1.195999 1.213394 1.230789 1.248183
## [95,] 1.121469 1.139069 1.156670 1.174270 1.191871 1.209471 1.227071 1.244672
## [96,] 1.116518 1.134324 1.152130 1.169936 1.187742 1.205548 1.223354 1.241160
## [97,] 1.111566 1.129578 1.147590 1.165602 1.183614 1.201625 1.219637 1.237649
## [98,] 1.106615 1.124832 1.143050 1.161267 1.179485 1.197703 1.215920 1.234138
## [99,] 1.101664 1.120087 1.138510 1.156933 1.175356 1.193780 1.212203 1.230626
## [,9] [,10] [,11] [,12] [,13] [,14] [,15] [,16]
## [1,] 1.573008 1.571271 1.569535 1.567799 1.566062 1.564326 1.562589 1.560853
## [2,] 1.569702 1.568171 1.566641 1.565110 1.563579 1.562049 1.560518 1.558987
## [3,] 1.566396 1.565071 1.563746 1.562421 1.561096 1.559772 1.558447 1.557122
## [4,] 1.563091 1.561971 1.560852 1.559733 1.558614 1.557494 1.556375 1.555256
## [5,] 1.559785 1.558871 1.557958 1.557044 1.556131 1.555217 1.554304 1.553390
## [6,] 1.556479 1.555771 1.555064 1.554356 1.553648 1.552940 1.552232 1.551524
## [7,] 1.553173 1.552671 1.552169 1.551667 1.551165 1.550663 1.550161 1.549659
## [8,] 1.549868 1.549571 1.549275 1.548979 1.548682 1.548386 1.548089 1.547793
## [9,] 1.546562 1.546471 1.546381 1.546290 1.546199 1.546109 1.546018 1.545927
## [10,] 1.543256 1.543371 1.543486 1.543601 1.543716 1.543832 1.543947 1.544062
## [11,] 1.539951 1.540271 1.540592 1.540913 1.541234 1.541554 1.541875 1.542196
## [12,] 1.536645 1.537171 1.537698 1.538224 1.538751 1.539277 1.539804 1.540330
## [13,] 1.533339 1.534071 1.534804 1.535536 1.536268 1.537000 1.537732 1.538464
## [14,] 1.530034 1.530971 1.531909 1.532847 1.533785 1.534723 1.535661 1.536599
## [15,] 1.526728 1.527871 1.529015 1.530159 1.531302 1.532446 1.533589 1.534733
## [16,] 1.523422 1.524772 1.526121 1.527470 1.528819 1.530169 1.531518 1.532867
## [17,] 1.520117 1.521672 1.523227 1.524782 1.526337 1.527892 1.529446 1.531001
## [18,] 1.516811 1.518572 1.520332 1.522093 1.523854 1.525614 1.527375 1.529136
## [19,] 1.513505 1.515472 1.517438 1.519404 1.521371 1.523337 1.525304 1.527270
## [20,] 1.510199 1.512372 1.514544 1.516716 1.518888 1.521060 1.523232 1.525404
## [21,] 1.506894 1.509272 1.511649 1.514027 1.516405 1.518783 1.521161 1.523539
## [22,] 1.503588 1.506172 1.508755 1.511339 1.513922 1.516506 1.519089 1.521673
## [23,] 1.500282 1.503072 1.505861 1.508650 1.511439 1.514229 1.517018 1.519807
## [24,] 1.496977 1.499972 1.502967 1.505962 1.508957 1.511951 1.514946 1.517941
## [25,] 1.493671 1.496872 1.500072 1.503273 1.506474 1.509674 1.512875 1.516076
## [26,] 1.490365 1.493772 1.497178 1.500584 1.503991 1.507397 1.510804 1.514210
## [27,] 1.487060 1.490672 1.494284 1.497896 1.501508 1.505120 1.508732 1.512344
## [28,] 1.483754 1.487572 1.491389 1.495207 1.499025 1.502843 1.506661 1.510479
## [29,] 1.480448 1.484472 1.488495 1.492519 1.496542 1.500566 1.504589 1.508613
## [30,] 1.477142 1.481372 1.485601 1.489830 1.494059 1.498289 1.502518 1.506747
## [31,] 1.473837 1.478272 1.482707 1.487142 1.491577 1.496011 1.500446 1.504881
## [32,] 1.470531 1.475172 1.479812 1.484453 1.489094 1.493734 1.498375 1.503016
## [33,] 1.467225 1.472072 1.476918 1.481764 1.486611 1.491457 1.496304 1.501150
## [34,] 1.463920 1.468972 1.474024 1.479076 1.484128 1.489180 1.494232 1.499284
## [35,] 1.460614 1.465872 1.471130 1.476387 1.481645 1.486903 1.492161 1.497418
## [36,] 1.457308 1.462772 1.468235 1.473699 1.479162 1.484626 1.490089 1.495553
## [37,] 1.454003 1.459672 1.465341 1.471010 1.476679 1.482349 1.488018 1.493687
## [38,] 1.450697 1.456572 1.462447 1.468322 1.474197 1.480071 1.485946 1.491821
## [39,] 1.447391 1.453472 1.459552 1.465633 1.471714 1.477794 1.483875 1.489956
## [40,] 1.444086 1.450372 1.456658 1.462944 1.469231 1.475517 1.481803 1.488090
## [41,] 1.440780 1.447272 1.453764 1.460256 1.466748 1.473240 1.479732 1.486224
## [42,] 1.437474 1.444172 1.450870 1.457567 1.464265 1.470963 1.477661 1.484358
## [43,] 1.434168 1.441072 1.447975 1.454879 1.461782 1.468686 1.475589 1.482493
## [44,] 1.430863 1.437972 1.445081 1.452190 1.459299 1.466409 1.473518 1.480627
## [45,] 1.427557 1.434872 1.442187 1.449502 1.456817 1.464131 1.471446 1.478761
## [46,] 1.424251 1.431772 1.439293 1.446813 1.454334 1.461854 1.469375 1.476895
## [47,] 1.420946 1.428672 1.436398 1.444125 1.451851 1.459577 1.467303 1.475030
## [48,] 1.417640 1.425572 1.433504 1.441436 1.449368 1.457300 1.465232 1.473164
## [49,] 1.414334 1.422472 1.430610 1.438747 1.446885 1.455023 1.463161 1.471298
## [50,] 1.411029 1.419372 1.427715 1.436059 1.444402 1.452746 1.461089 1.469433
## [51,] 1.407723 1.416272 1.424821 1.433370 1.441919 1.450469 1.459018 1.467567
## [52,] 1.404417 1.413172 1.421927 1.430682 1.439437 1.448191 1.456946 1.465701
## [53,] 1.401111 1.410072 1.419033 1.427993 1.436954 1.445914 1.454875 1.463835
## [54,] 1.397806 1.406972 1.416138 1.425305 1.434471 1.443637 1.452803 1.461970
## [55,] 1.394500 1.403872 1.413244 1.422616 1.431988 1.441360 1.450732 1.460104
## [56,] 1.391194 1.400772 1.410350 1.419927 1.429505 1.439083 1.448661 1.458238
## [57,] 1.387889 1.397672 1.407455 1.417239 1.427022 1.436806 1.446589 1.456372
## [58,] 1.384583 1.394572 1.404561 1.414550 1.424539 1.434529 1.444518 1.454507
## [59,] 1.381277 1.391472 1.401667 1.411862 1.422057 1.432251 1.442446 1.452641
## [60,] 1.377972 1.388372 1.398773 1.409173 1.419574 1.429974 1.440375 1.450775
## [61,] 1.374666 1.385272 1.395878 1.406485 1.417091 1.427697 1.438303 1.448910
## [62,] 1.371360 1.382172 1.392984 1.403796 1.414608 1.425420 1.436232 1.447044
## [63,] 1.368054 1.379072 1.390090 1.401107 1.412125 1.423143 1.434160 1.445178
## [64,] 1.364749 1.375972 1.387196 1.398419 1.409642 1.420866 1.432089 1.443312
## [65,] 1.361443 1.372872 1.384301 1.395730 1.407159 1.418589 1.430018 1.441447
## [66,] 1.358137 1.369772 1.381407 1.393042 1.404677 1.416311 1.427946 1.439581
## [67,] 1.354832 1.366672 1.378513 1.390353 1.402194 1.414034 1.425875 1.437715
## [68,] 1.351526 1.363572 1.375618 1.387665 1.399711 1.411757 1.423803 1.435850
## [69,] 1.348220 1.360472 1.372724 1.384976 1.397228 1.409480 1.421732 1.433984
## [70,] 1.344915 1.357372 1.369830 1.382288 1.394745 1.407203 1.419660 1.432118
## [71,] 1.341609 1.354272 1.366936 1.379599 1.392262 1.404926 1.417589 1.430252
## [72,] 1.338303 1.351172 1.364041 1.376910 1.389779 1.402648 1.415518 1.428387
## [73,] 1.334998 1.348072 1.361147 1.374222 1.387297 1.400371 1.413446 1.426521
## [74,] 1.331692 1.344972 1.358253 1.371533 1.384814 1.398094 1.411375 1.424655
## [75,] 1.328386 1.341872 1.355358 1.368845 1.382331 1.395817 1.409303 1.422789
## [76,] 1.325080 1.338772 1.352464 1.366156 1.379848 1.393540 1.407232 1.420924
## [77,] 1.321775 1.335672 1.349570 1.363468 1.377365 1.391263 1.405160 1.419058
## [78,] 1.318469 1.332572 1.346676 1.360779 1.374882 1.388986 1.403089 1.417192
## [79,] 1.315163 1.329472 1.343781 1.358090 1.372399 1.386708 1.401018 1.415327
## [80,] 1.311858 1.326372 1.340887 1.355402 1.369917 1.384431 1.398946 1.413461
## [81,] 1.308552 1.323272 1.337993 1.352713 1.367434 1.382154 1.396875 1.411595
## [82,] 1.305246 1.320172 1.335099 1.350025 1.364951 1.379877 1.394803 1.409729
## [83,] 1.301941 1.317072 1.332204 1.347336 1.362468 1.377600 1.392732 1.407864
## [84,] 1.298635 1.313972 1.329310 1.344648 1.359985 1.375323 1.390660 1.405998
## [85,] 1.295329 1.310872 1.326416 1.341959 1.357502 1.373046 1.388589 1.404132
## [86,] 1.292023 1.307772 1.323521 1.339270 1.355019 1.370768 1.386517 1.402266
## [87,] 1.288718 1.304672 1.320627 1.336582 1.352537 1.368491 1.384446 1.400401
## [88,] 1.285412 1.301572 1.317733 1.333893 1.350054 1.366214 1.382375 1.398535
## [89,] 1.282106 1.298472 1.314839 1.331205 1.347571 1.363937 1.380303 1.396669
## [90,] 1.278801 1.295373 1.311944 1.328516 1.345088 1.361660 1.378232 1.394804
## [91,] 1.275495 1.292273 1.309050 1.325828 1.342605 1.359383 1.376160 1.392938
## [92,] 1.272189 1.289173 1.306156 1.323139 1.340122 1.357106 1.374089 1.391072
## [93,] 1.268884 1.286073 1.303262 1.320450 1.337639 1.354828 1.372017 1.389206
## [94,] 1.265578 1.282973 1.300367 1.317762 1.335157 1.352551 1.369946 1.387341
## [95,] 1.262272 1.279873 1.297473 1.315073 1.332674 1.350274 1.367875 1.385475
## [96,] 1.258966 1.276773 1.294579 1.312385 1.330191 1.347997 1.365803 1.383609
## [97,] 1.255661 1.273673 1.291684 1.309696 1.327708 1.345720 1.363732 1.381743
## [98,] 1.252355 1.270573 1.288790 1.307008 1.325225 1.343443 1.361660 1.379878
## [99,] 1.249049 1.267473 1.285896 1.304319 1.322742 1.341166 1.359589 1.378012
## [,17] [,18] [,19] [,20] [,21] [,22] [,23] [,24]
## [1,] 1.559117 1.557380 1.555644 1.553908 1.552171 1.550435 1.548698 1.546962
## [2,] 1.557457 1.555926 1.554395 1.552865 1.551334 1.549803 1.548273 1.546742
## [3,] 1.555797 1.554472 1.553147 1.551822 1.550497 1.549172 1.547847 1.546522
## [4,] 1.554137 1.553017 1.551898 1.550779 1.549660 1.548540 1.547421 1.546302
## [5,] 1.552477 1.551563 1.550650 1.549736 1.548823 1.547909 1.546995 1.546082
## [6,] 1.550817 1.550109 1.549401 1.548693 1.547985 1.547278 1.546570 1.545862
## [7,] 1.549157 1.548655 1.548152 1.547650 1.547148 1.546646 1.546144 1.545642
## [8,] 1.547497 1.547200 1.546904 1.546607 1.546311 1.546015 1.545718 1.545422
## [9,] 1.545837 1.545746 1.545655 1.545565 1.545474 1.545383 1.545292 1.545202
## [10,] 1.544177 1.544292 1.544407 1.544522 1.544637 1.544752 1.544867 1.544982
## [11,] 1.542517 1.542837 1.543158 1.543479 1.543799 1.544120 1.544441 1.544762
## [12,] 1.540857 1.541383 1.541909 1.542436 1.542962 1.543489 1.544015 1.544542
## [13,] 1.539197 1.539929 1.540661 1.541393 1.542125 1.542857 1.543589 1.544322
## [14,] 1.537537 1.538474 1.539412 1.540350 1.541288 1.542226 1.543164 1.544102
## [15,] 1.535877 1.537020 1.538164 1.539307 1.540451 1.541594 1.542738 1.543882
## [16,] 1.534216 1.535566 1.536915 1.538264 1.539614 1.540963 1.542312 1.543661
## [17,] 1.532556 1.534111 1.535666 1.537221 1.538776 1.540331 1.541886 1.543441
## [18,] 1.530896 1.532657 1.534418 1.536179 1.537939 1.539700 1.541461 1.543221
## [19,] 1.529236 1.531203 1.533169 1.535136 1.537102 1.539069 1.541035 1.543001
## [20,] 1.527576 1.529749 1.531921 1.534093 1.536265 1.538437 1.540609 1.542781
## [21,] 1.525916 1.528294 1.530672 1.533050 1.535428 1.537806 1.540183 1.542561
## [22,] 1.524256 1.526840 1.529423 1.532007 1.534591 1.537174 1.539758 1.542341
## [23,] 1.522596 1.525386 1.528175 1.530964 1.533753 1.536543 1.539332 1.542121
## [24,] 1.520936 1.523931 1.526926 1.529921 1.532916 1.535911 1.538906 1.541901
## [25,] 1.519276 1.522477 1.525678 1.528878 1.532079 1.535280 1.538480 1.541681
## [26,] 1.517616 1.521023 1.524429 1.527836 1.531242 1.534648 1.538055 1.541461
## [27,] 1.515956 1.519568 1.523181 1.526793 1.530405 1.534017 1.537629 1.541241
## [28,] 1.514296 1.518114 1.521932 1.525750 1.529568 1.533385 1.537203 1.541021
## [29,] 1.512636 1.516660 1.520683 1.524707 1.528730 1.532754 1.536777 1.540801
## [30,] 1.510976 1.515206 1.519435 1.523664 1.527893 1.532122 1.536352 1.540581
## [31,] 1.509316 1.513751 1.518186 1.522621 1.527056 1.531491 1.535926 1.540361
## [32,] 1.507656 1.512297 1.516938 1.521578 1.526219 1.530860 1.535500 1.540141
## [33,] 1.505996 1.510843 1.515689 1.520535 1.525382 1.530228 1.535074 1.539921
## [34,] 1.504336 1.509388 1.514440 1.519492 1.524545 1.529597 1.534649 1.539701
## [35,] 1.502676 1.507934 1.513192 1.518450 1.523707 1.528965 1.534223 1.539481
## [36,] 1.501016 1.506480 1.511943 1.517407 1.522870 1.528334 1.533797 1.539261
## [37,] 1.499356 1.505025 1.510695 1.516364 1.522033 1.527702 1.533371 1.539041
## [38,] 1.497696 1.503571 1.509446 1.515321 1.521196 1.527071 1.532946 1.538821
## [39,] 1.496036 1.502117 1.508197 1.514278 1.520359 1.526439 1.532520 1.538600
## [40,] 1.494376 1.500662 1.506949 1.513235 1.519521 1.525808 1.532094 1.538380
## [41,] 1.492716 1.499208 1.505700 1.512192 1.518684 1.525176 1.531668 1.538160
## [42,] 1.491056 1.497754 1.504452 1.511149 1.517847 1.524545 1.531243 1.537940
## [43,] 1.489396 1.496300 1.503203 1.510106 1.517010 1.523913 1.530817 1.537720
## [44,] 1.487736 1.494845 1.501954 1.509064 1.516173 1.523282 1.530391 1.537500
## [45,] 1.486076 1.493391 1.500706 1.508021 1.515336 1.522650 1.529965 1.537280
## [46,] 1.484416 1.491937 1.499457 1.506978 1.514498 1.522019 1.529540 1.537060
## [47,] 1.482756 1.490482 1.498209 1.505935 1.513661 1.521388 1.529114 1.536840
## [48,] 1.481096 1.489028 1.496960 1.504892 1.512824 1.520756 1.528688 1.536620
## [49,] 1.479436 1.487574 1.495711 1.503849 1.511987 1.520125 1.528262 1.536400
## [50,] 1.477776 1.486119 1.494463 1.502806 1.511150 1.519493 1.527837 1.536180
## [51,] 1.476116 1.484665 1.493214 1.501763 1.510313 1.518862 1.527411 1.535960
## [52,] 1.474456 1.483211 1.491966 1.500721 1.509475 1.518230 1.526985 1.535740
## [53,] 1.472796 1.481757 1.490717 1.499678 1.508638 1.517599 1.526559 1.535520
## [54,] 1.471136 1.480302 1.489468 1.498635 1.507801 1.516967 1.526134 1.535300
## [55,] 1.469476 1.478848 1.488220 1.497592 1.506964 1.516336 1.525708 1.535080
## [56,] 1.467816 1.477394 1.486971 1.496549 1.506127 1.515704 1.525282 1.534860
## [57,] 1.466156 1.475939 1.485723 1.495506 1.505290 1.515073 1.524856 1.534640
## [58,] 1.464496 1.474485 1.484474 1.494463 1.504452 1.514441 1.524431 1.534420
## [59,] 1.462836 1.473031 1.483226 1.493420 1.503615 1.513810 1.524005 1.534200
## [60,] 1.461176 1.471576 1.481977 1.492377 1.502778 1.513179 1.523579 1.533980
## [61,] 1.459516 1.470122 1.480728 1.491335 1.501941 1.512547 1.523153 1.533760
## [62,] 1.457856 1.468668 1.479480 1.490292 1.501104 1.511916 1.522728 1.533540
## [63,] 1.456196 1.467213 1.478231 1.489249 1.500266 1.511284 1.522302 1.533319
## [64,] 1.454536 1.465759 1.476983 1.488206 1.499429 1.510653 1.521876 1.533099
## [65,] 1.452876 1.464305 1.475734 1.487163 1.498592 1.510021 1.521450 1.532879
## [66,] 1.451216 1.462851 1.474485 1.486120 1.497755 1.509390 1.521025 1.532659
## [67,] 1.449556 1.461396 1.473237 1.485077 1.496918 1.508758 1.520599 1.532439
## [68,] 1.447896 1.459942 1.471988 1.484034 1.496081 1.508127 1.520173 1.532219
## [69,] 1.446236 1.458488 1.470740 1.482992 1.495243 1.507495 1.519747 1.531999
## [70,] 1.444576 1.457033 1.469491 1.481949 1.494406 1.506864 1.519322 1.531779
## [71,] 1.442916 1.455579 1.468242 1.480906 1.493569 1.506232 1.518896 1.531559
## [72,] 1.441256 1.454125 1.466994 1.479863 1.492732 1.505601 1.518470 1.531339
## [73,] 1.439596 1.452670 1.465745 1.478820 1.491895 1.504970 1.518044 1.531119
## [74,] 1.437936 1.451216 1.464497 1.477777 1.491058 1.504338 1.517619 1.530899
## [75,] 1.436276 1.449762 1.463248 1.476734 1.490220 1.503707 1.517193 1.530679
## [76,] 1.434616 1.448308 1.461999 1.475691 1.489383 1.503075 1.516767 1.530459
## [77,] 1.432956 1.446853 1.460751 1.474648 1.488546 1.502444 1.516341 1.530239
## [78,] 1.431296 1.445399 1.459502 1.473606 1.487709 1.501812 1.515916 1.530019
## [79,] 1.429636 1.443945 1.458254 1.472563 1.486872 1.501181 1.515490 1.529799
## [80,] 1.427976 1.442490 1.457005 1.471520 1.486035 1.500549 1.515064 1.529579
## [81,] 1.426316 1.441036 1.455756 1.470477 1.485197 1.499918 1.514638 1.529359
## [82,] 1.424656 1.439582 1.454508 1.469434 1.484360 1.499286 1.514212 1.529139
## [83,] 1.422996 1.438127 1.453259 1.468391 1.483523 1.498655 1.513787 1.528919
## [84,] 1.421335 1.436673 1.452011 1.467348 1.482686 1.498023 1.513361 1.528699
## [85,] 1.419675 1.435219 1.450762 1.466305 1.481849 1.497392 1.512935 1.528479
## [86,] 1.418015 1.433764 1.449513 1.465262 1.481011 1.496760 1.512509 1.528258
## [87,] 1.416355 1.432310 1.448265 1.464220 1.480174 1.496129 1.512084 1.528038
## [88,] 1.414695 1.430856 1.447016 1.463177 1.479337 1.495498 1.511658 1.527818
## [89,] 1.413035 1.429402 1.445768 1.462134 1.478500 1.494866 1.511232 1.527598
## [90,] 1.411375 1.427947 1.444519 1.461091 1.477663 1.494235 1.510806 1.527378
## [91,] 1.409715 1.426493 1.443271 1.460048 1.476826 1.493603 1.510381 1.527158
## [92,] 1.408055 1.425039 1.442022 1.459005 1.475988 1.492972 1.509955 1.526938
## [93,] 1.406395 1.423584 1.440773 1.457962 1.475151 1.492340 1.509529 1.526718
## [94,] 1.404735 1.422130 1.439525 1.456919 1.474314 1.491709 1.509103 1.526498
## [95,] 1.403075 1.420676 1.438276 1.455877 1.473477 1.491077 1.508678 1.526278
## [96,] 1.401415 1.419221 1.437028 1.454834 1.472640 1.490446 1.508252 1.526058
## [97,] 1.399755 1.417767 1.435779 1.453791 1.471803 1.489814 1.507826 1.525838
## [98,] 1.398095 1.416313 1.434530 1.452748 1.470965 1.489183 1.507400 1.525618
## [99,] 1.396435 1.414859 1.433282 1.451705 1.470128 1.488551 1.506975 1.525398
## [,25] [,26] [,27] [,28] [,29] [,30] [,31] [,32]
## [1,] 1.545226 1.543489 1.541753 1.540017 1.538280 1.536544 1.534808 1.533071
## [2,] 1.545211 1.543681 1.542150 1.540619 1.539089 1.537558 1.536027 1.534497
## [3,] 1.545197 1.543872 1.542547 1.541222 1.539897 1.538572 1.537247 1.535922
## [4,] 1.545183 1.544064 1.542944 1.541825 1.540706 1.539587 1.538467 1.537348
## [5,] 1.545168 1.544255 1.543341 1.542428 1.541514 1.540601 1.539687 1.538774
## [6,] 1.545154 1.544446 1.543738 1.543031 1.542323 1.541615 1.540907 1.540199
## [7,] 1.545140 1.544638 1.544136 1.543633 1.543131 1.542629 1.542127 1.541625
## [8,] 1.545125 1.544829 1.544533 1.544236 1.543940 1.543643 1.543347 1.543051
## [9,] 1.545111 1.545020 1.544930 1.544839 1.544748 1.544658 1.544567 1.544476
## [10,] 1.545097 1.545212 1.545327 1.545442 1.545557 1.545672 1.545787 1.545902
## [11,] 1.545082 1.545403 1.545724 1.546045 1.546365 1.546686 1.547007 1.547328
## [12,] 1.545068 1.545595 1.546121 1.546647 1.547174 1.547700 1.548227 1.548753
## [13,] 1.545054 1.545786 1.546518 1.547250 1.547982 1.548715 1.549447 1.550179
## [14,] 1.545039 1.545977 1.546915 1.547853 1.548791 1.549729 1.550667 1.551604
## [15,] 1.545025 1.546169 1.547312 1.548456 1.549599 1.550743 1.551887 1.553030
## [16,] 1.545011 1.546360 1.547709 1.549059 1.550408 1.551757 1.553106 1.554456
## [17,] 1.544996 1.546551 1.548106 1.549661 1.551216 1.552771 1.554326 1.555881
## [18,] 1.544982 1.546743 1.548504 1.550264 1.552025 1.553786 1.555546 1.557307
## [19,] 1.544968 1.546934 1.548901 1.550867 1.552833 1.554800 1.556766 1.558733
## [20,] 1.544953 1.547126 1.549298 1.551470 1.553642 1.555814 1.557986 1.560158
## [21,] 1.544939 1.547317 1.549695 1.552073 1.554450 1.556828 1.559206 1.561584
## [22,] 1.544925 1.547508 1.550092 1.552675 1.555259 1.557842 1.560426 1.563010
## [23,] 1.544910 1.547700 1.550489 1.553278 1.556067 1.558857 1.561646 1.564435
## [24,] 1.544896 1.547891 1.550886 1.553881 1.556876 1.559871 1.562866 1.565861
## [25,] 1.544882 1.548082 1.551283 1.554484 1.557684 1.560885 1.564086 1.567287
## [26,] 1.544867 1.548274 1.551680 1.555087 1.558493 1.561899 1.565306 1.568712
## [27,] 1.544853 1.548465 1.552077 1.555689 1.559301 1.562914 1.566526 1.570138
## [28,] 1.544839 1.548657 1.552474 1.556292 1.560110 1.563928 1.567746 1.571563
## [29,] 1.544824 1.548848 1.552871 1.556895 1.560919 1.564942 1.568966 1.572989
## [30,] 1.544810 1.549039 1.553269 1.557498 1.561727 1.565956 1.570185 1.574415
## [31,] 1.544796 1.549231 1.553666 1.558101 1.562536 1.566970 1.571405 1.575840
## [32,] 1.544781 1.549422 1.554063 1.558703 1.563344 1.567985 1.572625 1.577266
## [33,] 1.544767 1.549613 1.554460 1.559306 1.564153 1.568999 1.573845 1.578692
## [34,] 1.544753 1.549805 1.554857 1.559909 1.564961 1.570013 1.575065 1.580117
## [35,] 1.544738 1.549996 1.555254 1.560512 1.565770 1.571027 1.576285 1.581543
## [36,] 1.544724 1.550188 1.555651 1.561115 1.566578 1.572042 1.577505 1.582969
## [37,] 1.544710 1.550379 1.556048 1.561717 1.567387 1.573056 1.578725 1.584394
## [38,] 1.544695 1.550570 1.556445 1.562320 1.568195 1.574070 1.579945 1.585820
## [39,] 1.544681 1.550762 1.556842 1.562923 1.569004 1.575084 1.581165 1.587245
## [40,] 1.544667 1.550953 1.557239 1.563526 1.569812 1.576098 1.582385 1.588671
## [41,] 1.544652 1.551144 1.557637 1.564129 1.570621 1.577113 1.583605 1.590097
## [42,] 1.544638 1.551336 1.558034 1.564731 1.571429 1.578127 1.584825 1.591522
## [43,] 1.544624 1.551527 1.558431 1.565334 1.572238 1.579141 1.586045 1.592948
## [44,] 1.544609 1.551719 1.558828 1.565937 1.573046 1.580155 1.587264 1.594374
## [45,] 1.544595 1.551910 1.559225 1.566540 1.573855 1.581170 1.588484 1.595799
## [46,] 1.544581 1.552101 1.559622 1.567143 1.574663 1.582184 1.589704 1.597225
## [47,] 1.544566 1.552293 1.560019 1.567745 1.575472 1.583198 1.590924 1.598651
## [48,] 1.544552 1.552484 1.560416 1.568348 1.576280 1.584212 1.592144 1.600076
## [49,] 1.544538 1.552676 1.560813 1.568951 1.577089 1.585226 1.593364 1.601502
## [50,] 1.544523 1.552867 1.561210 1.569554 1.577897 1.586241 1.594584 1.602927
## [51,] 1.544509 1.553058 1.561607 1.570157 1.578706 1.587255 1.595804 1.604353
## [52,] 1.544495 1.553250 1.562004 1.570759 1.579514 1.588269 1.597024 1.605779
## [53,] 1.544480 1.553441 1.562402 1.571362 1.580323 1.589283 1.598244 1.607204
## [54,] 1.544466 1.553632 1.562799 1.571965 1.581131 1.590297 1.599464 1.608630
## [55,] 1.544452 1.553824 1.563196 1.572568 1.581940 1.591312 1.600684 1.610056
## [56,] 1.544437 1.554015 1.563593 1.573171 1.582748 1.592326 1.601904 1.611481
## [57,] 1.544423 1.554207 1.563990 1.573773 1.583557 1.593340 1.603124 1.612907
## [58,] 1.544409 1.554398 1.564387 1.574376 1.584365 1.594354 1.604343 1.614333
## [59,] 1.544394 1.554589 1.564784 1.574979 1.585174 1.595369 1.605563 1.615758
## [60,] 1.544380 1.554781 1.565181 1.575582 1.585982 1.596383 1.606783 1.617184
## [61,] 1.544366 1.554972 1.565578 1.576185 1.586791 1.597397 1.608003 1.618610
## [62,] 1.544351 1.555163 1.565975 1.576787 1.587599 1.598411 1.609223 1.620035
## [63,] 1.544337 1.555355 1.566372 1.577390 1.588408 1.599425 1.610443 1.621461
## [64,] 1.544323 1.555546 1.566770 1.577993 1.589216 1.600440 1.611663 1.622886
## [65,] 1.544308 1.555738 1.567167 1.578596 1.590025 1.601454 1.612883 1.624312
## [66,] 1.544294 1.555929 1.567564 1.579199 1.590833 1.602468 1.614103 1.625738
## [67,] 1.544280 1.556120 1.567961 1.579801 1.591642 1.603482 1.615323 1.627163
## [68,] 1.544265 1.556312 1.568358 1.580404 1.592450 1.604497 1.616543 1.628589
## [69,] 1.544251 1.556503 1.568755 1.581007 1.593259 1.605511 1.617763 1.630015
## [70,] 1.544237 1.556694 1.569152 1.581610 1.594067 1.606525 1.618983 1.631440
## [71,] 1.544222 1.556886 1.569549 1.582213 1.594876 1.607539 1.620203 1.632866
## [72,] 1.544208 1.557077 1.569946 1.582815 1.595684 1.608553 1.621422 1.634292
## [73,] 1.544194 1.557269 1.570343 1.583418 1.596493 1.609568 1.622642 1.635717
## [74,] 1.544179 1.557460 1.570740 1.584021 1.597301 1.610582 1.623862 1.637143
## [75,] 1.544165 1.557651 1.571138 1.584624 1.598110 1.611596 1.625082 1.638568
## [76,] 1.544151 1.557843 1.571535 1.585227 1.598918 1.612610 1.626302 1.639994
## [77,] 1.544136 1.558034 1.571932 1.585829 1.599727 1.613625 1.627522 1.641420
## [78,] 1.544122 1.558225 1.572329 1.586432 1.600535 1.614639 1.628742 1.642845
## [79,] 1.544108 1.558417 1.572726 1.587035 1.601344 1.615653 1.629962 1.644271
## [80,] 1.544093 1.558608 1.573123 1.587638 1.602152 1.616667 1.631182 1.645697
## [81,] 1.544079 1.558800 1.573520 1.588241 1.602961 1.617681 1.632402 1.647122
## [82,] 1.544065 1.558991 1.573917 1.588843 1.603769 1.618696 1.633622 1.648548
## [83,] 1.544050 1.559182 1.574314 1.589446 1.604578 1.619710 1.634842 1.649974
## [84,] 1.544036 1.559374 1.574711 1.590049 1.605386 1.620724 1.636062 1.651399
## [85,] 1.544022 1.559565 1.575108 1.590652 1.606195 1.621738 1.637282 1.652825
## [86,] 1.544007 1.559756 1.575505 1.591254 1.607003 1.622752 1.638502 1.654251
## [87,] 1.543993 1.559948 1.575903 1.591857 1.607812 1.623767 1.639721 1.655676
## [88,] 1.543979 1.560139 1.576300 1.592460 1.608621 1.624781 1.640941 1.657102
## [89,] 1.543964 1.560331 1.576697 1.593063 1.609429 1.625795 1.642161 1.658527
## [90,] 1.543950 1.560522 1.577094 1.593666 1.610238 1.626809 1.643381 1.659953
## [91,] 1.543936 1.560713 1.577491 1.594268 1.611046 1.627824 1.644601 1.661379
## [92,] 1.543921 1.560905 1.577888 1.594871 1.611855 1.628838 1.645821 1.662804
## [93,] 1.543907 1.561096 1.578285 1.595474 1.612663 1.629852 1.647041 1.664230
## [94,] 1.543893 1.561288 1.578682 1.596077 1.613472 1.630866 1.648261 1.665656
## [95,] 1.543878 1.561479 1.579079 1.596680 1.614280 1.631880 1.649481 1.667081
## [96,] 1.543864 1.561670 1.579476 1.597282 1.615089 1.632895 1.650701 1.668507
## [97,] 1.543850 1.561862 1.579873 1.597885 1.615897 1.633909 1.651921 1.669933
## [98,] 1.543835 1.562053 1.580271 1.598488 1.616706 1.634923 1.653141 1.671358
## [99,] 1.543821 1.562244 1.580668 1.599091 1.617514 1.635937 1.654361 1.672784
## [,33] [,34] [,35] [,36] [,37] [,38] [,39] [,40]
## [1,] 1.531335 1.529598 1.527862 1.526126 1.524389 1.522653 1.520917 1.519180
## [2,] 1.532966 1.531435 1.529905 1.528374 1.526843 1.525313 1.523782 1.522252
## [3,] 1.534597 1.533273 1.531948 1.530623 1.529298 1.527973 1.526648 1.525323
## [4,] 1.536229 1.535110 1.533990 1.532871 1.531752 1.530633 1.529513 1.528394
## [5,] 1.537860 1.536947 1.536033 1.535120 1.534206 1.533293 1.532379 1.531465
## [6,] 1.539492 1.538784 1.538076 1.537368 1.536660 1.535952 1.535245 1.534537
## [7,] 1.541123 1.540621 1.540119 1.539617 1.539114 1.538612 1.538110 1.537608
## [8,] 1.542754 1.542458 1.542161 1.541865 1.541569 1.541272 1.540976 1.540679
## [9,] 1.544386 1.544295 1.544204 1.544114 1.544023 1.543932 1.543841 1.543751
## [10,] 1.546017 1.546132 1.546247 1.546362 1.546477 1.546592 1.546707 1.546822
## [11,] 1.547648 1.547969 1.548290 1.548610 1.548931 1.549252 1.549573 1.549893
## [12,] 1.549280 1.549806 1.550333 1.550859 1.551385 1.551912 1.552438 1.552965
## [13,] 1.550911 1.551643 1.552375 1.553107 1.553840 1.554572 1.555304 1.556036
## [14,] 1.552542 1.553480 1.554418 1.555356 1.556294 1.557232 1.558170 1.559107
## [15,] 1.554174 1.555317 1.556461 1.557604 1.558748 1.559892 1.561035 1.562179
## [16,] 1.555805 1.557154 1.558504 1.559853 1.561202 1.562551 1.563901 1.565250
## [17,] 1.557436 1.558991 1.560546 1.562101 1.563656 1.565211 1.566766 1.568321
## [18,] 1.559068 1.560828 1.562589 1.564350 1.566111 1.567871 1.569632 1.571393
## [19,] 1.560699 1.562665 1.564632 1.566598 1.568565 1.570531 1.572498 1.574464
## [20,] 1.562330 1.564503 1.566675 1.568847 1.571019 1.573191 1.575363 1.577535
## [21,] 1.563962 1.566340 1.568717 1.571095 1.573473 1.575851 1.578229 1.580607
## [22,] 1.565593 1.568177 1.570760 1.573344 1.575927 1.578511 1.581094 1.583678
## [23,] 1.567224 1.570014 1.572803 1.575592 1.578382 1.581171 1.583960 1.586749
## [24,] 1.568856 1.571851 1.574846 1.577841 1.580836 1.583831 1.586826 1.589821
## [25,] 1.570487 1.573688 1.576889 1.580089 1.583290 1.586491 1.589691 1.592892
## [26,] 1.572119 1.575525 1.578931 1.582338 1.585744 1.589150 1.592557 1.595963
## [27,] 1.573750 1.577362 1.580974 1.584586 1.588198 1.591810 1.595422 1.599035
## [28,] 1.575381 1.579199 1.583017 1.586835 1.590652 1.594470 1.598288 1.602106
## [29,] 1.577013 1.581036 1.585060 1.589083 1.593107 1.597130 1.601154 1.605177
## [30,] 1.578644 1.582873 1.587102 1.591332 1.595561 1.599790 1.604019 1.608249
## [31,] 1.580275 1.584710 1.589145 1.593580 1.598015 1.602450 1.606885 1.611320
## [32,] 1.581907 1.586547 1.591188 1.595829 1.600469 1.605110 1.609751 1.614391
## [33,] 1.583538 1.588384 1.593231 1.598077 1.602923 1.607770 1.612616 1.617462
## [34,] 1.585169 1.590221 1.595273 1.600326 1.605378 1.610430 1.615482 1.620534
## [35,] 1.586801 1.592058 1.597316 1.602574 1.607832 1.613090 1.618347 1.623605
## [36,] 1.588432 1.593896 1.599359 1.604822 1.610286 1.615749 1.621213 1.626676
## [37,] 1.590063 1.595733 1.601402 1.607071 1.612740 1.618409 1.624079 1.629748
## [38,] 1.591695 1.597570 1.603445 1.609319 1.615194 1.621069 1.626944 1.632819
## [39,] 1.593326 1.599407 1.605487 1.611568 1.617649 1.623729 1.629810 1.635890
## [40,] 1.594957 1.601244 1.607530 1.613816 1.620103 1.626389 1.632675 1.638962
## [41,] 1.596589 1.603081 1.609573 1.616065 1.622557 1.629049 1.635541 1.642033
## [42,] 1.598220 1.604918 1.611616 1.618313 1.625011 1.631709 1.638407 1.645104
## [43,] 1.599851 1.606755 1.613658 1.620562 1.627465 1.634369 1.641272 1.648176
## [44,] 1.601483 1.608592 1.615701 1.622810 1.629920 1.637029 1.644138 1.651247
## [45,] 1.603114 1.610429 1.617744 1.625059 1.632374 1.639689 1.647003 1.654318
## [46,] 1.604746 1.612266 1.619787 1.627307 1.634828 1.642348 1.649869 1.657390
## [47,] 1.606377 1.614103 1.621829 1.629556 1.637282 1.645008 1.652735 1.660461
## [48,] 1.608008 1.615940 1.623872 1.631804 1.639736 1.647668 1.655600 1.663532
## [49,] 1.609640 1.617777 1.625915 1.634053 1.642190 1.650328 1.658466 1.666604
## [50,] 1.611271 1.619614 1.627958 1.636301 1.644645 1.652988 1.661332 1.669675
## [51,] 1.612902 1.621451 1.630001 1.638550 1.647099 1.655648 1.664197 1.672746
## [52,] 1.614534 1.623288 1.632043 1.640798 1.649553 1.658308 1.667063 1.675818
## [53,] 1.616165 1.625126 1.634086 1.643047 1.652007 1.660968 1.669928 1.678889
## [54,] 1.617796 1.626963 1.636129 1.645295 1.654461 1.663628 1.672794 1.681960
## [55,] 1.619428 1.628800 1.638172 1.647544 1.656916 1.666288 1.675660 1.685032
## [56,] 1.621059 1.630637 1.640214 1.649792 1.659370 1.668947 1.678525 1.688103
## [57,] 1.622690 1.632474 1.642257 1.652041 1.661824 1.671607 1.681391 1.691174
## [58,] 1.624322 1.634311 1.644300 1.654289 1.664278 1.674267 1.684256 1.694246
## [59,] 1.625953 1.636148 1.646343 1.656538 1.666732 1.676927 1.687122 1.697317
## [60,] 1.627584 1.637985 1.648385 1.658786 1.669187 1.679587 1.689988 1.700388
## [61,] 1.629216 1.639822 1.650428 1.661035 1.671641 1.682247 1.692853 1.703459
## [62,] 1.630847 1.641659 1.652471 1.663283 1.674095 1.684907 1.695719 1.706531
## [63,] 1.632478 1.643496 1.654514 1.665531 1.676549 1.687567 1.698584 1.709602
## [64,] 1.634110 1.645333 1.656557 1.667780 1.679003 1.690227 1.701450 1.712673
## [65,] 1.635741 1.647170 1.658599 1.670028 1.681458 1.692887 1.704316 1.715745
## [66,] 1.637373 1.649007 1.660642 1.672277 1.683912 1.695546 1.707181 1.718816
## [67,] 1.639004 1.650844 1.662685 1.674525 1.686366 1.698206 1.710047 1.721887
## [68,] 1.640635 1.652681 1.664728 1.676774 1.688820 1.700866 1.712913 1.724959
## [69,] 1.642267 1.654518 1.666770 1.679022 1.691274 1.703526 1.715778 1.728030
## [70,] 1.643898 1.656356 1.668813 1.681271 1.693728 1.706186 1.718644 1.731101
## [71,] 1.645529 1.658193 1.670856 1.683519 1.696183 1.708846 1.721509 1.734173
## [72,] 1.647161 1.660030 1.672899 1.685768 1.698637 1.711506 1.724375 1.737244
## [73,] 1.648792 1.661867 1.674941 1.688016 1.701091 1.714166 1.727241 1.740315
## [74,] 1.650423 1.663704 1.676984 1.690265 1.703545 1.716826 1.730106 1.743387
## [75,] 1.652055 1.665541 1.679027 1.692513 1.705999 1.719486 1.732972 1.746458
## [76,] 1.653686 1.667378 1.681070 1.694762 1.708454 1.722146 1.735837 1.749529
## [77,] 1.655317 1.669215 1.683113 1.697010 1.710908 1.724805 1.738703 1.752601
## [78,] 1.656949 1.671052 1.685155 1.699259 1.713362 1.727465 1.741569 1.755672
## [79,] 1.658580 1.672889 1.687198 1.701507 1.715816 1.730125 1.744434 1.758743
## [80,] 1.660211 1.674726 1.689241 1.703756 1.718270 1.732785 1.747300 1.761815
## [81,] 1.661843 1.676563 1.691284 1.706004 1.720725 1.735445 1.750165 1.764886
## [82,] 1.663474 1.678400 1.693326 1.708253 1.723179 1.738105 1.753031 1.767957
## [83,] 1.665105 1.680237 1.695369 1.710501 1.725633 1.740765 1.755897 1.771029
## [84,] 1.666737 1.682074 1.697412 1.712750 1.728087 1.743425 1.758762 1.774100
## [85,] 1.668368 1.683911 1.699455 1.714998 1.730541 1.746085 1.761628 1.777171
## [86,] 1.670000 1.685749 1.701498 1.717247 1.732996 1.748745 1.764494 1.780243
## [87,] 1.671631 1.687586 1.703540 1.719495 1.735450 1.751404 1.767359 1.783314
## [88,] 1.673262 1.689423 1.705583 1.721743 1.737904 1.754064 1.770225 1.786385
## [89,] 1.674894 1.691260 1.707626 1.723992 1.740358 1.756724 1.773090 1.789456
## [90,] 1.676525 1.693097 1.709669 1.726240 1.742812 1.759384 1.775956 1.792528
## [91,] 1.678156 1.694934 1.711711 1.728489 1.745266 1.762044 1.778822 1.795599
## [92,] 1.679788 1.696771 1.713754 1.730737 1.747721 1.764704 1.781687 1.798670
## [93,] 1.681419 1.698608 1.715797 1.732986 1.750175 1.767364 1.784553 1.801742
## [94,] 1.683050 1.700445 1.717840 1.735234 1.752629 1.770024 1.787418 1.804813
## [95,] 1.684682 1.702282 1.719882 1.737483 1.755083 1.772684 1.790284 1.807884
## [96,] 1.686313 1.704119 1.721925 1.739731 1.757537 1.775344 1.793150 1.810956
## [97,] 1.687944 1.705956 1.723968 1.741980 1.759992 1.778003 1.796015 1.814027
## [98,] 1.689576 1.707793 1.726011 1.744228 1.762446 1.780663 1.798881 1.817098
## [99,] 1.691207 1.709630 1.728054 1.746477 1.764900 1.783323 1.801746 1.820170
## [,41] [,42] [,43] [,44] [,45] [,46] [,47] [,48]
## [1,] 1.517444 1.515707 1.513971 1.512235 1.510498 1.508762 1.507026 1.505289
## [2,] 1.520721 1.519190 1.517660 1.516129 1.514598 1.513068 1.511537 1.510006
## [3,] 1.523998 1.522673 1.521348 1.520023 1.518698 1.517373 1.516048 1.514723
## [4,] 1.527275 1.526156 1.525036 1.523917 1.522798 1.521679 1.520559 1.519440
## [5,] 1.530552 1.529638 1.528725 1.527811 1.526898 1.525984 1.525071 1.524157
## [6,] 1.533829 1.533121 1.532413 1.531706 1.530998 1.530290 1.529582 1.528874
## [7,] 1.537106 1.536604 1.536102 1.535600 1.535098 1.534595 1.534093 1.533591
## [8,] 1.540383 1.540087 1.539790 1.539494 1.539197 1.538901 1.538605 1.538308
## [9,] 1.543660 1.543569 1.543479 1.543388 1.543297 1.543207 1.543116 1.543025
## [10,] 1.546937 1.547052 1.547167 1.547282 1.547397 1.547512 1.547627 1.547742
## [11,] 1.550214 1.550535 1.550856 1.551176 1.551497 1.551818 1.552139 1.552459
## [12,] 1.553491 1.554018 1.554544 1.555071 1.555597 1.556123 1.556650 1.557176
## [13,] 1.556768 1.557500 1.558233 1.558965 1.559697 1.560429 1.561161 1.561893
## [14,] 1.560045 1.560983 1.561921 1.562859 1.563797 1.564735 1.565672 1.566610
## [15,] 1.563322 1.564466 1.565609 1.566753 1.567897 1.569040 1.570184 1.571327
## [16,] 1.566599 1.567949 1.569298 1.570647 1.571996 1.573346 1.574695 1.576044
## [17,] 1.569876 1.571431 1.572986 1.574541 1.576096 1.577651 1.579206 1.580761
## [18,] 1.573153 1.574914 1.576675 1.578435 1.580196 1.581957 1.583718 1.585478
## [19,] 1.576430 1.578397 1.580363 1.582330 1.584296 1.586262 1.588229 1.590195
## [20,] 1.579707 1.581880 1.584052 1.586224 1.588396 1.590568 1.592740 1.594912
## [21,] 1.582984 1.585362 1.587740 1.590118 1.592496 1.594874 1.597251 1.599629
## [22,] 1.586261 1.588845 1.591429 1.594012 1.596596 1.599179 1.601763 1.604346
## [23,] 1.589539 1.592328 1.595117 1.597906 1.600696 1.603485 1.606274 1.609063
## [24,] 1.592816 1.595811 1.598805 1.601800 1.604795 1.607790 1.610785 1.613780
## [25,] 1.596093 1.599293 1.602494 1.605695 1.608895 1.612096 1.615297 1.618497
## [26,] 1.599370 1.602776 1.606182 1.609589 1.612995 1.616402 1.619808 1.623214
## [27,] 1.602647 1.606259 1.609871 1.613483 1.617095 1.620707 1.624319 1.627931
## [28,] 1.605924 1.609741 1.613559 1.617377 1.621195 1.625013 1.628831 1.632648
## [29,] 1.609201 1.613224 1.617248 1.621271 1.625295 1.629318 1.633342 1.637365
## [30,] 1.612478 1.616707 1.620936 1.625165 1.629395 1.633624 1.637853 1.642082
## [31,] 1.615755 1.620190 1.624625 1.629060 1.633495 1.637929 1.642364 1.646799
## [32,] 1.619032 1.623672 1.628313 1.632954 1.637594 1.642235 1.646876 1.651516
## [33,] 1.622309 1.627155 1.632002 1.636848 1.641694 1.646541 1.651387 1.656233
## [34,] 1.625586 1.630638 1.635690 1.640742 1.645794 1.650846 1.655898 1.660950
## [35,] 1.628863 1.634121 1.639378 1.644636 1.649894 1.655152 1.660410 1.665667
## [36,] 1.632140 1.637603 1.643067 1.648530 1.653994 1.659457 1.664921 1.670384
## [37,] 1.635417 1.641086 1.646755 1.652425 1.658094 1.663763 1.669432 1.675101
## [38,] 1.638694 1.644569 1.650444 1.656319 1.662194 1.668069 1.673943 1.679818
## [39,] 1.641971 1.648052 1.654132 1.660213 1.666294 1.672374 1.678455 1.684535
## [40,] 1.645248 1.651534 1.657821 1.664107 1.670393 1.676680 1.682966 1.689252
## [41,] 1.648525 1.655017 1.661509 1.668001 1.674493 1.680985 1.687477 1.693969
## [42,] 1.651802 1.658500 1.665198 1.671895 1.678593 1.685291 1.691989 1.698686
## [43,] 1.655079 1.661983 1.668886 1.675790 1.682693 1.689596 1.696500 1.703403
## [44,] 1.658356 1.665465 1.672575 1.679684 1.686793 1.693902 1.701011 1.708120
## [45,] 1.661633 1.668948 1.676263 1.683578 1.690893 1.698208 1.705523 1.712837
## [46,] 1.664910 1.672431 1.679951 1.687472 1.694993 1.702513 1.710034 1.717554
## [47,] 1.668187 1.675914 1.683640 1.691366 1.699092 1.706819 1.714545 1.722271
## [48,] 1.671464 1.679396 1.687328 1.695260 1.703192 1.711124 1.719056 1.726988
## [49,] 1.674741 1.682879 1.691017 1.699155 1.707292 1.715430 1.723568 1.731705
## [50,] 1.678018 1.686362 1.694705 1.703049 1.711392 1.719736 1.728079 1.736422
## [51,] 1.681295 1.689845 1.698394 1.706943 1.715492 1.724041 1.732590 1.741139
## [52,] 1.684572 1.693327 1.702082 1.710837 1.719592 1.728347 1.737102 1.745856
## [53,] 1.687849 1.696810 1.705771 1.714731 1.723692 1.732652 1.741613 1.750573
## [54,] 1.691127 1.700293 1.709459 1.718625 1.727792 1.736958 1.746124 1.755290
## [55,] 1.694404 1.703776 1.713148 1.722519 1.731891 1.741263 1.750635 1.760007
## [56,] 1.697681 1.707258 1.716836 1.726414 1.735991 1.745569 1.755147 1.764724
## [57,] 1.700958 1.710741 1.720524 1.730308 1.740091 1.749875 1.759658 1.769441
## [58,] 1.704235 1.714224 1.724213 1.734202 1.744191 1.754180 1.764169 1.774158
## [59,] 1.707512 1.717706 1.727901 1.738096 1.748291 1.758486 1.768681 1.778875
## [60,] 1.710789 1.721189 1.731590 1.741990 1.752391 1.762791 1.773192 1.783592
## [61,] 1.714066 1.724672 1.735278 1.745884 1.756491 1.767097 1.777703 1.788309
## [62,] 1.717343 1.728155 1.738967 1.749779 1.760591 1.771403 1.782214 1.793026
## [63,] 1.720620 1.731637 1.742655 1.753673 1.764690 1.775708 1.786726 1.797743
## [64,] 1.723897 1.735120 1.746344 1.757567 1.768790 1.780014 1.791237 1.802460
## [65,] 1.727174 1.738603 1.750032 1.761461 1.772890 1.784319 1.795748 1.807177
## [66,] 1.730451 1.742086 1.753720 1.765355 1.776990 1.788625 1.800260 1.811894
## [67,] 1.733728 1.745568 1.757409 1.769249 1.781090 1.792930 1.804771 1.816611
## [68,] 1.737005 1.749051 1.761097 1.773144 1.785190 1.797236 1.809282 1.821328
## [69,] 1.740282 1.752534 1.764786 1.777038 1.789290 1.801542 1.813794 1.826045
## [70,] 1.743559 1.756017 1.768474 1.780932 1.793390 1.805847 1.818305 1.830762
## [71,] 1.746836 1.759499 1.772163 1.784826 1.797489 1.810153 1.822816 1.835479
## [72,] 1.750113 1.762982 1.775851 1.788720 1.801589 1.814458 1.827327 1.840196
## [73,] 1.753390 1.766465 1.779540 1.792614 1.805689 1.818764 1.831839 1.844913
## [74,] 1.756667 1.769948 1.783228 1.796509 1.809789 1.823070 1.836350 1.849630
## [75,] 1.759944 1.773430 1.786917 1.800403 1.813889 1.827375 1.840861 1.854347
## [76,] 1.763221 1.776913 1.790605 1.804297 1.817989 1.831681 1.845373 1.859065
## [77,] 1.766498 1.780396 1.794293 1.808191 1.822089 1.835986 1.849884 1.863782
## [78,] 1.769775 1.783879 1.797982 1.812085 1.826189 1.840292 1.854395 1.868499
## [79,] 1.773052 1.787361 1.801670 1.815979 1.830288 1.844597 1.858906 1.873216
## [80,] 1.776329 1.790844 1.805359 1.819874 1.834388 1.848903 1.863418 1.877933
## [81,] 1.779606 1.794327 1.809047 1.823768 1.838488 1.853209 1.867929 1.882650
## [82,] 1.782883 1.797810 1.812736 1.827662 1.842588 1.857514 1.872440 1.887367
## [83,] 1.786160 1.801292 1.816424 1.831556 1.846688 1.861820 1.876952 1.892084
## [84,] 1.789437 1.804775 1.820113 1.835450 1.850788 1.866125 1.881463 1.896801
## [85,] 1.792714 1.808258 1.823801 1.839344 1.854888 1.870431 1.885974 1.901518
## [86,] 1.795992 1.811741 1.827490 1.843239 1.858988 1.874737 1.890486 1.906235
## [87,] 1.799269 1.815223 1.831178 1.847133 1.863087 1.879042 1.894997 1.910952
## [88,] 1.802546 1.818706 1.834866 1.851027 1.867187 1.883348 1.899508 1.915669
## [89,] 1.805823 1.822189 1.838555 1.854921 1.871287 1.887653 1.904019 1.920386
## [90,] 1.809100 1.825671 1.842243 1.858815 1.875387 1.891959 1.908531 1.925103
## [91,] 1.812377 1.829154 1.845932 1.862709 1.879487 1.896264 1.913042 1.929820
## [92,] 1.815654 1.832637 1.849620 1.866604 1.883587 1.900570 1.917553 1.934537
## [93,] 1.818931 1.836120 1.853309 1.870498 1.887687 1.904876 1.922065 1.939254
## [94,] 1.822208 1.839602 1.856997 1.874392 1.891787 1.909181 1.926576 1.943971
## [95,] 1.825485 1.843085 1.860686 1.878286 1.895886 1.913487 1.931087 1.948688
## [96,] 1.828762 1.846568 1.864374 1.882180 1.899986 1.917792 1.935598 1.953405
## [97,] 1.832039 1.850051 1.868063 1.886074 1.904086 1.922098 1.940110 1.958122
## [98,] 1.835316 1.853533 1.871751 1.889968 1.908186 1.926404 1.944621 1.962839
## [99,] 1.838593 1.857016 1.875439 1.893863 1.912286 1.930709 1.949132 1.967556
## [,49] [,50] [,51] [,52] [,53] [,54] [,55] [,56]
## [1,] 1.503553 1.501816 1.500080 1.498344 1.496607 1.494871 1.493135 1.491398
## [2,] 1.508476 1.506945 1.505414 1.503884 1.502353 1.500822 1.499292 1.497761
## [3,] 1.513398 1.512073 1.510748 1.509423 1.508098 1.506774 1.505449 1.504124
## [4,] 1.518321 1.517202 1.516083 1.514963 1.513844 1.512725 1.511606 1.510486
## [5,] 1.523244 1.522330 1.521417 1.520503 1.519590 1.518676 1.517763 1.516849
## [6,] 1.528166 1.527459 1.526751 1.526043 1.525335 1.524627 1.523920 1.523212
## [7,] 1.533089 1.532587 1.532085 1.531583 1.531081 1.530579 1.530076 1.529574
## [8,] 1.538012 1.537715 1.537419 1.537123 1.536826 1.536530 1.536233 1.535937
## [9,] 1.542935 1.542844 1.542753 1.542663 1.542572 1.542481 1.542390 1.542300
## [10,] 1.547857 1.547972 1.548087 1.548202 1.548317 1.548432 1.548547 1.548662
## [11,] 1.552780 1.553101 1.553421 1.553742 1.554063 1.554384 1.554704 1.555025
## [12,] 1.557703 1.558229 1.558756 1.559282 1.559808 1.560335 1.560861 1.561388
## [13,] 1.562625 1.563358 1.564090 1.564822 1.565554 1.566286 1.567018 1.567750
## [14,] 1.567548 1.568486 1.569424 1.570362 1.571300 1.572237 1.573175 1.574113
## [15,] 1.572471 1.573614 1.574758 1.575902 1.577045 1.578189 1.579332 1.580476
## [16,] 1.577394 1.578743 1.580092 1.581441 1.582791 1.584140 1.585489 1.586839
## [17,] 1.582316 1.583871 1.585426 1.586981 1.588536 1.590091 1.591646 1.593201
## [18,] 1.587239 1.589000 1.590760 1.592521 1.594282 1.596043 1.597803 1.599564
## [19,] 1.592162 1.594128 1.596095 1.598061 1.600027 1.601994 1.603960 1.605927
## [20,] 1.597084 1.599257 1.601429 1.603601 1.605773 1.607945 1.610117 1.612289
## [21,] 1.602007 1.604385 1.606763 1.609141 1.611518 1.613896 1.616274 1.618652
## [22,] 1.606930 1.609513 1.612097 1.614680 1.617264 1.619848 1.622431 1.625015
## [23,] 1.611853 1.614642 1.617431 1.620220 1.623010 1.625799 1.628588 1.631377
## [24,] 1.616775 1.619770 1.622765 1.625760 1.628755 1.631750 1.634745 1.637740
## [25,] 1.621698 1.624899 1.628099 1.631300 1.634501 1.637701 1.640902 1.644103
## [26,] 1.626621 1.630027 1.633433 1.636840 1.640246 1.643653 1.647059 1.650465
## [27,] 1.631543 1.635156 1.638768 1.642380 1.645992 1.649604 1.653216 1.656828
## [28,] 1.636466 1.640284 1.644102 1.647920 1.651737 1.655555 1.659373 1.663191
## [29,] 1.641389 1.645412 1.649436 1.653459 1.657483 1.661506 1.665530 1.669553
## [30,] 1.646312 1.650541 1.654770 1.658999 1.663228 1.667458 1.671687 1.675916
## [31,] 1.651234 1.655669 1.660104 1.664539 1.668974 1.673409 1.677844 1.682279
## [32,] 1.656157 1.660798 1.665438 1.670079 1.674720 1.679360 1.684001 1.688642
## [33,] 1.661080 1.665926 1.670772 1.675619 1.680465 1.685311 1.690158 1.695004
## [34,] 1.666002 1.671054 1.676107 1.681159 1.686211 1.691263 1.696315 1.701367
## [35,] 1.670925 1.676183 1.681441 1.686698 1.691956 1.697214 1.702472 1.707730
## [36,] 1.675848 1.681311 1.686775 1.692238 1.697702 1.703165 1.708629 1.714092
## [37,] 1.680771 1.686440 1.692109 1.697778 1.703447 1.709117 1.714786 1.720455
## [38,] 1.685693 1.691568 1.697443 1.703318 1.709193 1.715068 1.720943 1.726818
## [39,] 1.690616 1.696697 1.702777 1.708858 1.714938 1.721019 1.727100 1.733180
## [40,] 1.695539 1.701825 1.708111 1.714398 1.720684 1.726970 1.733257 1.739543
## [41,] 1.700461 1.706953 1.713445 1.719938 1.726430 1.732922 1.739414 1.745906
## [42,] 1.705384 1.712082 1.718780 1.725477 1.732175 1.738873 1.745571 1.752268
## [43,] 1.710307 1.717210 1.724114 1.731017 1.737921 1.744824 1.751728 1.758631
## [44,] 1.715230 1.722339 1.729448 1.736557 1.743666 1.750775 1.757885 1.764994
## [45,] 1.720152 1.727467 1.734782 1.742097 1.749412 1.756727 1.764042 1.771356
## [46,] 1.725075 1.732596 1.740116 1.747637 1.755157 1.762678 1.770199 1.777719
## [47,] 1.729998 1.737724 1.745450 1.753177 1.760903 1.768629 1.776356 1.784082
## [48,] 1.734920 1.742852 1.750784 1.758716 1.766648 1.774580 1.782512 1.790444
## [49,] 1.739843 1.747981 1.756119 1.764256 1.772394 1.780532 1.788669 1.796807
## [50,] 1.744766 1.753109 1.761453 1.769796 1.778140 1.786483 1.794826 1.803170
## [51,] 1.749689 1.758238 1.766787 1.775336 1.783885 1.792434 1.800983 1.809533
## [52,] 1.754611 1.763366 1.772121 1.780876 1.789631 1.798386 1.807140 1.815895
## [53,] 1.759534 1.768495 1.777455 1.786416 1.795376 1.804337 1.813297 1.822258
## [54,] 1.764457 1.773623 1.782789 1.791956 1.801122 1.810288 1.819454 1.828621
## [55,] 1.769379 1.778751 1.788123 1.797495 1.806867 1.816239 1.825611 1.834983
## [56,] 1.774302 1.783880 1.793458 1.803035 1.812613 1.822191 1.831768 1.841346
## [57,] 1.779225 1.789008 1.798792 1.808575 1.818358 1.828142 1.837925 1.847709
## [58,] 1.784148 1.794137 1.804126 1.814115 1.824104 1.834093 1.844082 1.854071
## [59,] 1.789070 1.799265 1.809460 1.819655 1.829850 1.840044 1.850239 1.860434
## [60,] 1.793993 1.804394 1.814794 1.825195 1.835595 1.845996 1.856396 1.866797
## [61,] 1.798916 1.809522 1.820128 1.830734 1.841341 1.851947 1.862553 1.873159
## [62,] 1.803838 1.814650 1.825462 1.836274 1.847086 1.857898 1.868710 1.879522
## [63,] 1.808761 1.819779 1.830796 1.841814 1.852832 1.863849 1.874867 1.885885
## [64,] 1.813684 1.824907 1.836131 1.847354 1.858577 1.869801 1.881024 1.892247
## [65,] 1.818607 1.830036 1.841465 1.852894 1.864323 1.875752 1.887181 1.898610
## [66,] 1.823529 1.835164 1.846799 1.858434 1.870068 1.881703 1.893338 1.904973
## [67,] 1.828452 1.840292 1.852133 1.863973 1.875814 1.887655 1.899495 1.911336
## [68,] 1.833375 1.845421 1.857467 1.869513 1.881560 1.893606 1.905652 1.917698
## [69,] 1.838297 1.850549 1.862801 1.875053 1.887305 1.899557 1.911809 1.924061
## [70,] 1.843220 1.855678 1.868135 1.880593 1.893051 1.905508 1.917966 1.930424
## [71,] 1.848143 1.860806 1.873470 1.886133 1.898796 1.911460 1.924123 1.936786
## [72,] 1.853066 1.865935 1.878804 1.891673 1.904542 1.917411 1.930280 1.943149
## [73,] 1.857988 1.871063 1.884138 1.897213 1.910287 1.923362 1.936437 1.949512
## [74,] 1.862911 1.876191 1.889472 1.902752 1.916033 1.929313 1.942594 1.955874
## [75,] 1.867834 1.881320 1.894806 1.908292 1.921778 1.935265 1.948751 1.962237
## [76,] 1.872756 1.886448 1.900140 1.913832 1.927524 1.941216 1.954908 1.968600
## [77,] 1.877679 1.891577 1.905474 1.919372 1.933270 1.947167 1.961065 1.974962
## [78,] 1.882602 1.896705 1.910808 1.924912 1.939015 1.953118 1.967222 1.981325
## [79,] 1.887525 1.901834 1.916143 1.930452 1.944761 1.959070 1.973379 1.987688
## [80,] 1.892447 1.906962 1.921477 1.935991 1.950506 1.965021 1.979536 1.994050
## [81,] 1.897370 1.912090 1.926811 1.941531 1.956252 1.970972 1.985693 2.000413
## [82,] 1.902293 1.917219 1.932145 1.947071 1.961997 1.976923 1.991850 2.006776
## [83,] 1.907215 1.922347 1.937479 1.952611 1.967743 1.982875 1.998007 2.013139
## [84,] 1.912138 1.927476 1.942813 1.958151 1.973488 1.988826 2.004164 2.019501
## [85,] 1.917061 1.932604 1.948147 1.963691 1.979234 1.994777 2.010321 2.025864
## [86,] 1.921984 1.937733 1.953482 1.969231 1.984980 2.000729 2.016478 2.032227
## [87,] 1.926906 1.942861 1.958816 1.974770 1.990725 2.006680 2.022635 2.038589
## [88,] 1.931829 1.947989 1.964150 1.980310 1.996471 2.012631 2.028792 2.044952
## [89,] 1.936752 1.953118 1.969484 1.985850 2.002216 2.018582 2.034948 2.051315
## [90,] 1.941674 1.958246 1.974818 1.991390 2.007962 2.024534 2.041105 2.057677
## [91,] 1.946597 1.963375 1.980152 1.996930 2.013707 2.030485 2.047262 2.064040
## [92,] 1.951520 1.968503 1.985486 2.002470 2.019453 2.036436 2.053419 2.070403
## [93,] 1.956443 1.973632 1.990820 2.008009 2.025198 2.042387 2.059576 2.076765
## [94,] 1.961365 1.978760 1.996155 2.013549 2.030944 2.048339 2.065733 2.083128
## [95,] 1.966288 1.983888 2.001489 2.019089 2.036690 2.054290 2.071890 2.089491
## [96,] 1.971211 1.989017 2.006823 2.024629 2.042435 2.060241 2.078047 2.095853
## [97,] 1.976133 1.994145 2.012157 2.030169 2.048181 2.066192 2.084204 2.102216
## [98,] 1.981056 1.999274 2.017491 2.035709 2.053926 2.072144 2.090361 2.108579
## [99,] 1.985979 2.004402 2.022825 2.041249 2.059672 2.078095 2.096518 2.114941
## [,57] [,58] [,59] [,60] [,61] [,62] [,63] [,64]
## [1,] 1.489662 1.487926 1.486189 1.484453 1.482716 1.480980 1.479244 1.477507
## [2,] 1.496230 1.494700 1.493169 1.491638 1.490108 1.488577 1.487046 1.485516
## [3,] 1.502799 1.501474 1.500149 1.498824 1.497499 1.496174 1.494849 1.493524
## [4,] 1.509367 1.508248 1.507129 1.506009 1.504890 1.503771 1.502652 1.501532
## [5,] 1.515935 1.515022 1.514108 1.513195 1.512281 1.511368 1.510454 1.509541
## [6,] 1.522504 1.521796 1.521088 1.520380 1.519673 1.518965 1.518257 1.517549
## [7,] 1.529072 1.528570 1.528068 1.527566 1.527064 1.526562 1.526060 1.525558
## [8,] 1.535641 1.535344 1.535048 1.534751 1.534455 1.534159 1.533862 1.533566
## [9,] 1.542209 1.542118 1.542028 1.541937 1.541846 1.541756 1.541665 1.541574
## [10,] 1.548777 1.548892 1.549008 1.549123 1.549238 1.549353 1.549468 1.549583
## [11,] 1.555346 1.555667 1.555987 1.556308 1.556629 1.556950 1.557270 1.557591
## [12,] 1.561914 1.562441 1.562967 1.563494 1.564020 1.564546 1.565073 1.565599
## [13,] 1.568483 1.569215 1.569947 1.570679 1.571411 1.572143 1.572876 1.573608
## [14,] 1.575051 1.575989 1.576927 1.577865 1.578802 1.579740 1.580678 1.581616
## [15,] 1.581619 1.582763 1.583907 1.585050 1.586194 1.587337 1.588481 1.589624
## [16,] 1.588188 1.589537 1.590886 1.592236 1.593585 1.594934 1.596284 1.597633
## [17,] 1.594756 1.596311 1.597866 1.599421 1.600976 1.602531 1.604086 1.605641
## [18,] 1.601325 1.603085 1.604846 1.606607 1.608367 1.610128 1.611889 1.613650
## [19,] 1.607893 1.609859 1.611826 1.613792 1.615759 1.617725 1.619692 1.621658
## [20,] 1.614461 1.616634 1.618806 1.620978 1.623150 1.625322 1.627494 1.629666
## [21,] 1.621030 1.623408 1.625785 1.628163 1.630541 1.632919 1.635297 1.637675
## [22,] 1.627598 1.630182 1.632765 1.635349 1.637932 1.640516 1.643099 1.645683
## [23,] 1.634167 1.636956 1.639745 1.642534 1.645324 1.648113 1.650902 1.653691
## [24,] 1.640735 1.643730 1.646725 1.649720 1.652715 1.655710 1.658705 1.661700
## [25,] 1.647303 1.650504 1.653705 1.656905 1.660106 1.663307 1.666507 1.669708
## [26,] 1.653872 1.657278 1.660685 1.664091 1.667497 1.670904 1.674310 1.677717
## [27,] 1.660440 1.664052 1.667664 1.671276 1.674889 1.678501 1.682113 1.685725
## [28,] 1.667009 1.670826 1.674644 1.678462 1.682280 1.686098 1.689915 1.693733
## [29,] 1.673577 1.677601 1.681624 1.685648 1.689671 1.693695 1.697718 1.701742
## [30,] 1.680145 1.684375 1.688604 1.692833 1.697062 1.701292 1.705521 1.709750
## [31,] 1.686714 1.691149 1.695584 1.700019 1.704454 1.708888 1.713323 1.717758
## [32,] 1.693282 1.697923 1.702563 1.707204 1.711845 1.716485 1.721126 1.725767
## [33,] 1.699851 1.704697 1.709543 1.714390 1.719236 1.724082 1.728929 1.733775
## [34,] 1.706419 1.711471 1.716523 1.721575 1.726627 1.731679 1.736731 1.741783
## [35,] 1.712987 1.718245 1.723503 1.728761 1.734018 1.739276 1.744534 1.749792
## [36,] 1.719556 1.725019 1.730483 1.735946 1.741410 1.746873 1.752337 1.757800
## [37,] 1.726124 1.731793 1.737463 1.743132 1.748801 1.754470 1.760139 1.765809
## [38,] 1.732693 1.738567 1.744442 1.750317 1.756192 1.762067 1.767942 1.773817
## [39,] 1.739261 1.745342 1.751422 1.757503 1.763583 1.769664 1.775745 1.781825
## [40,] 1.745829 1.752116 1.758402 1.764688 1.770975 1.777261 1.783547 1.789834
## [41,] 1.752398 1.758890 1.765382 1.771874 1.778366 1.784858 1.791350 1.797842
## [42,] 1.758966 1.765664 1.772362 1.779059 1.785757 1.792455 1.799153 1.805850
## [43,] 1.765535 1.772438 1.779341 1.786245 1.793148 1.800052 1.806955 1.813859
## [44,] 1.772103 1.779212 1.786321 1.793430 1.800540 1.807649 1.814758 1.821867
## [45,] 1.778671 1.785986 1.793301 1.800616 1.807931 1.815246 1.822561 1.829875
## [46,] 1.785240 1.792760 1.800281 1.807801 1.815322 1.822843 1.830363 1.837884
## [47,] 1.791808 1.799534 1.807261 1.814987 1.822713 1.830440 1.838166 1.845892
## [48,] 1.798377 1.806309 1.814241 1.822173 1.830105 1.838037 1.845969 1.853901
## [49,] 1.804945 1.813083 1.821220 1.829358 1.837496 1.845634 1.853771 1.861909
## [50,] 1.811513 1.819857 1.828200 1.836544 1.844887 1.853230 1.861574 1.869917
## [51,] 1.818082 1.826631 1.835180 1.843729 1.852278 1.860827 1.869377 1.877926
## [52,] 1.824650 1.833405 1.842160 1.850915 1.859670 1.868424 1.877179 1.885934
## [53,] 1.831218 1.840179 1.849140 1.858100 1.867061 1.876021 1.884982 1.893942
## [54,] 1.837787 1.846953 1.856119 1.865286 1.874452 1.883618 1.892785 1.901951
## [55,] 1.844355 1.853727 1.863099 1.872471 1.881843 1.891215 1.900587 1.909959
## [56,] 1.850924 1.860501 1.870079 1.879657 1.889234 1.898812 1.908390 1.917968
## [57,] 1.857492 1.867275 1.877059 1.886842 1.896626 1.906409 1.916193 1.925976
## [58,] 1.864060 1.874050 1.884039 1.894028 1.904017 1.914006 1.923995 1.933984
## [59,] 1.870629 1.880824 1.891019 1.901213 1.911408 1.921603 1.931798 1.941993
## [60,] 1.877197 1.887598 1.897998 1.908399 1.918799 1.929200 1.939600 1.950001
## [61,] 1.883766 1.894372 1.904978 1.915584 1.926191 1.936797 1.947403 1.958009
## [62,] 1.890334 1.901146 1.911958 1.922770 1.933582 1.944394 1.955206 1.966018
## [63,] 1.896902 1.907920 1.918938 1.929955 1.940973 1.951991 1.963008 1.974026
## [64,] 1.903471 1.914694 1.925918 1.937141 1.948364 1.959588 1.970811 1.982034
## [65,] 1.910039 1.921468 1.932897 1.944327 1.955756 1.967185 1.978614 1.990043
## [66,] 1.916608 1.928242 1.939877 1.951512 1.963147 1.974782 1.986416 1.998051
## [67,] 1.923176 1.935017 1.946857 1.958698 1.970538 1.982379 1.994219 2.006060
## [68,] 1.929744 1.941791 1.953837 1.965883 1.977929 1.989976 2.002022 2.014068
## [69,] 1.936313 1.948565 1.960817 1.973069 1.985321 1.997572 2.009824 2.022076
## [70,] 1.942881 1.955339 1.967797 1.980254 1.992712 2.005169 2.017627 2.030085
## [71,] 1.949450 1.962113 1.974776 1.987440 2.000103 2.012766 2.025430 2.038093
## [72,] 1.956018 1.968887 1.981756 1.994625 2.007494 2.020363 2.033232 2.046101
## [73,] 1.962586 1.975661 1.988736 2.001811 2.014885 2.027960 2.041035 2.054110
## [74,] 1.969155 1.982435 1.995716 2.008996 2.022277 2.035557 2.048838 2.062118
## [75,] 1.975723 1.989209 2.002696 2.016182 2.029668 2.043154 2.056640 2.070127
## [76,] 1.982292 1.995983 2.009675 2.023367 2.037059 2.050751 2.064443 2.078135
## [77,] 1.988860 2.002758 2.016655 2.030553 2.044450 2.058348 2.072246 2.086143
## [78,] 1.995428 2.009532 2.023635 2.037738 2.051842 2.065945 2.080048 2.094152
## [79,] 2.001997 2.016306 2.030615 2.044924 2.059233 2.073542 2.087851 2.102160
## [80,] 2.008565 2.023080 2.037595 2.052109 2.066624 2.081139 2.095654 2.110168
## [81,] 2.015134 2.029854 2.044574 2.059295 2.074015 2.088736 2.103456 2.118177
## [82,] 2.021702 2.036628 2.051554 2.066480 2.081407 2.096333 2.111259 2.126185
## [83,] 2.028270 2.043402 2.058534 2.073666 2.088798 2.103930 2.119062 2.134193
## [84,] 2.034839 2.050176 2.065514 2.080852 2.096189 2.111527 2.126864 2.142202
## [85,] 2.041407 2.056950 2.072494 2.088037 2.103580 2.119124 2.134667 2.150210
## [86,] 2.047976 2.063725 2.079474 2.095223 2.110972 2.126721 2.142470 2.158219
## [87,] 2.054544 2.070499 2.086453 2.102408 2.118363 2.134318 2.150272 2.166227
## [88,] 2.061112 2.077273 2.093433 2.109594 2.125754 2.141914 2.158075 2.174235
## [89,] 2.067681 2.084047 2.100413 2.116779 2.133145 2.149511 2.165878 2.182244
## [90,] 2.074249 2.090821 2.107393 2.123965 2.140537 2.157108 2.173680 2.190252
## [91,] 2.080818 2.097595 2.114373 2.131150 2.147928 2.164705 2.181483 2.198260
## [92,] 2.087386 2.104369 2.121352 2.138336 2.155319 2.172302 2.189286 2.206269
## [93,] 2.093954 2.111143 2.128332 2.145521 2.162710 2.179899 2.197088 2.214277
## [94,] 2.100523 2.117917 2.135312 2.152707 2.170101 2.187496 2.204891 2.222286
## [95,] 2.107091 2.124692 2.142292 2.159892 2.177493 2.195093 2.212693 2.230294
## [96,] 2.113660 2.131466 2.149272 2.167078 2.184884 2.202690 2.220496 2.238302
## [97,] 2.120228 2.138240 2.156252 2.174263 2.192275 2.210287 2.228299 2.246311
## [98,] 2.126796 2.145014 2.163231 2.181449 2.199666 2.217884 2.236101 2.254319
## [99,] 2.133365 2.151788 2.170211 2.188634 2.207058 2.225481 2.243904 2.262327
## [,65] [,66] [,67] [,68] [,69] [,70] [,71] [,72]
## [1,] 1.475771 1.474035 1.472298 1.470562 1.468825 1.467089 1.465353 1.463616
## [2,] 1.483985 1.482454 1.480924 1.479393 1.477862 1.476332 1.474801 1.473270
## [3,] 1.492199 1.490874 1.489549 1.488224 1.486899 1.485574 1.484249 1.482924
## [4,] 1.500413 1.499294 1.498175 1.497055 1.495936 1.494817 1.493698 1.492578
## [5,] 1.508627 1.507714 1.506800 1.505887 1.504973 1.504060 1.503146 1.502233
## [6,] 1.516841 1.516134 1.515426 1.514718 1.514010 1.513302 1.512594 1.511887
## [7,] 1.525055 1.524553 1.524051 1.523549 1.523047 1.522545 1.522043 1.521541
## [8,] 1.533269 1.532973 1.532677 1.532380 1.532084 1.531787 1.531491 1.531195
## [9,] 1.541484 1.541393 1.541302 1.541211 1.541121 1.541030 1.540939 1.540849
## [10,] 1.549698 1.549813 1.549928 1.550043 1.550158 1.550273 1.550388 1.550503
## [11,] 1.557912 1.558232 1.558553 1.558874 1.559195 1.559515 1.559836 1.560157
## [12,] 1.566126 1.566652 1.567179 1.567705 1.568232 1.568758 1.569284 1.569811
## [13,] 1.574340 1.575072 1.575804 1.576536 1.577268 1.578001 1.578733 1.579465
## [14,] 1.582554 1.583492 1.584430 1.585368 1.586305 1.587243 1.588181 1.589119
## [15,] 1.590768 1.591912 1.593055 1.594199 1.595342 1.596486 1.597629 1.598773
## [16,] 1.598982 1.600331 1.601681 1.603030 1.604379 1.605729 1.607078 1.608427
## [17,] 1.607196 1.608751 1.610306 1.611861 1.613416 1.614971 1.616526 1.618081
## [18,] 1.615410 1.617171 1.618932 1.620692 1.622453 1.624214 1.625974 1.627735
## [19,] 1.623624 1.625591 1.627557 1.629524 1.631490 1.633456 1.635423 1.637389
## [20,] 1.631838 1.634011 1.636183 1.638355 1.640527 1.642699 1.644871 1.647043
## [21,] 1.640052 1.642430 1.644808 1.647186 1.649564 1.651942 1.654320 1.656697
## [22,] 1.648267 1.650850 1.653434 1.656017 1.658601 1.661184 1.663768 1.666351
## [23,] 1.656481 1.659270 1.662059 1.664848 1.667638 1.670427 1.673216 1.676005
## [24,] 1.664695 1.667690 1.670685 1.673680 1.676675 1.679670 1.682665 1.685659
## [25,] 1.672909 1.676109 1.679310 1.682511 1.685712 1.688912 1.692113 1.695314
## [26,] 1.681123 1.684529 1.687936 1.691342 1.694748 1.698155 1.701561 1.704968
## [27,] 1.689337 1.692949 1.696561 1.700173 1.703785 1.707397 1.711010 1.714622
## [28,] 1.697551 1.701369 1.705187 1.709004 1.712822 1.716640 1.720458 1.724276
## [29,] 1.705765 1.709789 1.713812 1.717836 1.721859 1.725883 1.729906 1.733930
## [30,] 1.713979 1.718208 1.722438 1.726667 1.730896 1.735125 1.739355 1.743584
## [31,] 1.722193 1.726628 1.731063 1.735498 1.739933 1.744368 1.748803 1.753238
## [32,] 1.730407 1.735048 1.739689 1.744329 1.748970 1.753611 1.758251 1.762892
## [33,] 1.738621 1.743468 1.748314 1.753161 1.758007 1.762853 1.767700 1.772546
## [34,] 1.746836 1.751888 1.756940 1.761992 1.767044 1.772096 1.777148 1.782200
## [35,] 1.755050 1.760307 1.765565 1.770823 1.776081 1.781338 1.786596 1.791854
## [36,] 1.763264 1.768727 1.774191 1.779654 1.785118 1.790581 1.796045 1.801508
## [37,] 1.771478 1.777147 1.782816 1.788485 1.794155 1.799824 1.805493 1.811162
## [38,] 1.779692 1.785567 1.791442 1.797317 1.803191 1.809066 1.814941 1.820816
## [39,] 1.787906 1.793987 1.800067 1.806148 1.812228 1.818309 1.824390 1.830470
## [40,] 1.796120 1.802406 1.808693 1.814979 1.821265 1.827552 1.833838 1.840124
## [41,] 1.804334 1.810826 1.817318 1.823810 1.830302 1.836794 1.843286 1.849778
## [42,] 1.812548 1.819246 1.825944 1.832641 1.839339 1.846037 1.852735 1.859432
## [43,] 1.820762 1.827666 1.834569 1.841473 1.848376 1.855280 1.862183 1.869086
## [44,] 1.828976 1.836085 1.843195 1.850304 1.857413 1.864522 1.871631 1.878740
## [45,] 1.837190 1.844505 1.851820 1.859135 1.866450 1.873765 1.881080 1.888395
## [46,] 1.845404 1.852925 1.860446 1.867966 1.875487 1.883007 1.890528 1.898049
## [47,] 1.853619 1.861345 1.869071 1.876797 1.884524 1.892250 1.899976 1.907703
## [48,] 1.861833 1.869765 1.877697 1.885629 1.893561 1.901493 1.909425 1.917357
## [49,] 1.870047 1.878184 1.886322 1.894460 1.902598 1.910735 1.918873 1.927011
## [50,] 1.878261 1.886604 1.894948 1.903291 1.911634 1.919978 1.928321 1.936665
## [51,] 1.886475 1.895024 1.903573 1.912122 1.920671 1.929221 1.937770 1.946319
## [52,] 1.894689 1.903444 1.912199 1.920953 1.929708 1.938463 1.947218 1.955973
## [53,] 1.902903 1.911864 1.920824 1.929785 1.938745 1.947706 1.956666 1.965627
## [54,] 1.911117 1.920283 1.929450 1.938616 1.947782 1.956948 1.966115 1.975281
## [55,] 1.919331 1.928703 1.938075 1.947447 1.956819 1.966191 1.975563 1.984935
## [56,] 1.927545 1.937123 1.946701 1.956278 1.965856 1.975434 1.985011 1.994589
## [57,] 1.935759 1.945543 1.955326 1.965110 1.974893 1.984676 1.994460 2.004243
## [58,] 1.943973 1.953963 1.963952 1.973941 1.983930 1.993919 2.003908 2.013897
## [59,] 1.952187 1.962382 1.972577 1.982772 1.992967 2.003162 2.013356 2.023551
## [60,] 1.960402 1.970802 1.981203 1.991603 2.002004 2.012404 2.022805 2.033205
## [61,] 1.968616 1.979222 1.989828 2.000434 2.011041 2.021647 2.032253 2.042859
## [62,] 1.976830 1.987642 1.998454 2.009266 2.020078 2.030889 2.041701 2.052513
## [63,] 1.985044 1.996061 2.007079 2.018097 2.029114 2.040132 2.051150 2.062167
## [64,] 1.993258 2.004481 2.015705 2.026928 2.038151 2.049375 2.060598 2.071821
## [65,] 2.001472 2.012901 2.024330 2.035759 2.047188 2.058617 2.070046 2.081476
## [66,] 2.009686 2.021321 2.032956 2.044590 2.056225 2.067860 2.079495 2.091130
## [67,] 2.017900 2.029741 2.041581 2.053422 2.065262 2.077103 2.088943 2.100784
## [68,] 2.026114 2.038160 2.050207 2.062253 2.074299 2.086345 2.098391 2.110438
## [69,] 2.034328 2.046580 2.058832 2.071084 2.083336 2.095588 2.107840 2.120092
## [70,] 2.042542 2.055000 2.067458 2.079915 2.092373 2.104831 2.117288 2.129746
## [71,] 2.050756 2.063420 2.076083 2.088746 2.101410 2.114073 2.126736 2.139400
## [72,] 2.058970 2.071840 2.084709 2.097578 2.110447 2.123316 2.136185 2.149054
## [73,] 2.067185 2.080259 2.093334 2.106409 2.119484 2.132558 2.145633 2.158708
## [74,] 2.075399 2.088679 2.101960 2.115240 2.128521 2.141801 2.155082 2.168362
## [75,] 2.083613 2.097099 2.110585 2.124071 2.137557 2.151044 2.164530 2.178016
## [76,] 2.091827 2.105519 2.119211 2.132902 2.146594 2.160286 2.173978 2.187670
## [77,] 2.100041 2.113938 2.127836 2.141734 2.155631 2.169529 2.183427 2.197324
## [78,] 2.108255 2.122358 2.136462 2.150565 2.164668 2.178772 2.192875 2.206978
## [79,] 2.116469 2.130778 2.145087 2.159396 2.173705 2.188014 2.202323 2.216632
## [80,] 2.124683 2.139198 2.153713 2.168227 2.182742 2.197257 2.211772 2.226286
## [81,] 2.132897 2.147618 2.162338 2.177059 2.191779 2.206499 2.221220 2.235940
## [82,] 2.141111 2.156037 2.170964 2.185890 2.200816 2.215742 2.230668 2.245594
## [83,] 2.149325 2.164457 2.179589 2.194721 2.209853 2.224985 2.240117 2.255248
## [84,] 2.157539 2.172877 2.188215 2.203552 2.218890 2.234227 2.249565 2.264902
## [85,] 2.165754 2.181297 2.196840 2.212383 2.227927 2.243470 2.259013 2.274557
## [86,] 2.173968 2.189717 2.205466 2.221215 2.236964 2.252713 2.268462 2.284211
## [87,] 2.182182 2.198136 2.214091 2.230046 2.246001 2.261955 2.277910 2.293865
## [88,] 2.190396 2.206556 2.222717 2.238877 2.255037 2.271198 2.287358 2.303519
## [89,] 2.198610 2.214976 2.231342 2.247708 2.264074 2.280440 2.296807 2.313173
## [90,] 2.206824 2.223396 2.239968 2.256539 2.273111 2.289683 2.306255 2.322827
## [91,] 2.215038 2.231816 2.248593 2.265371 2.282148 2.298926 2.315703 2.332481
## [92,] 2.223252 2.240235 2.257219 2.274202 2.291185 2.308168 2.325152 2.342135
## [93,] 2.231466 2.248655 2.265844 2.283033 2.300222 2.317411 2.334600 2.351789
## [94,] 2.239680 2.257075 2.274470 2.291864 2.309259 2.326654 2.344048 2.361443
## [95,] 2.247894 2.265495 2.283095 2.300695 2.318296 2.335896 2.353497 2.371097
## [96,] 2.256108 2.273914 2.291721 2.309527 2.327333 2.345139 2.362945 2.380751
## [97,] 2.264322 2.282334 2.300346 2.318358 2.336370 2.354382 2.372393 2.390405
## [98,] 2.272537 2.290754 2.308972 2.327189 2.345407 2.363624 2.381842 2.400059
## [99,] 2.280751 2.299174 2.317597 2.336020 2.354444 2.372867 2.391290 2.409713
## [,73] [,74] [,75] [,76] [,77] [,78] [,79] [,80]
## [1,] 1.461880 1.460144 1.458407 1.456671 1.454934 1.453198 1.451462 1.449725
## [2,] 1.471740 1.470209 1.468678 1.467148 1.465617 1.464086 1.462556 1.461025
## [3,] 1.481599 1.480275 1.478950 1.477625 1.476300 1.474975 1.473650 1.472325
## [4,] 1.491459 1.490340 1.489221 1.488102 1.486982 1.485863 1.484744 1.483625
## [5,] 1.501319 1.500405 1.499492 1.498578 1.497665 1.496751 1.495838 1.494924
## [6,] 1.511179 1.510471 1.509763 1.509055 1.508347 1.507640 1.506932 1.506224
## [7,] 1.521039 1.520536 1.520034 1.519532 1.519030 1.518528 1.518026 1.517524
## [8,] 1.530898 1.530602 1.530305 1.530009 1.529713 1.529416 1.529120 1.528824
## [9,] 1.540758 1.540667 1.540577 1.540486 1.540395 1.540305 1.540214 1.540123
## [10,] 1.550618 1.550733 1.550848 1.550963 1.551078 1.551193 1.551308 1.551423
## [11,] 1.560478 1.560798 1.561119 1.561440 1.561761 1.562081 1.562402 1.562723
## [12,] 1.570337 1.570864 1.571390 1.571917 1.572443 1.572970 1.573496 1.574022
## [13,] 1.580197 1.580929 1.581661 1.582394 1.583126 1.583858 1.584590 1.585322
## [14,] 1.590057 1.590995 1.591933 1.592870 1.593808 1.594746 1.595684 1.596622
## [15,] 1.599917 1.601060 1.602204 1.603347 1.604491 1.605634 1.606778 1.607922
## [16,] 1.609776 1.611126 1.612475 1.613824 1.615174 1.616523 1.617872 1.619221
## [17,] 1.619636 1.621191 1.622746 1.624301 1.625856 1.627411 1.628966 1.630521
## [18,] 1.629496 1.631257 1.633017 1.634778 1.636539 1.638299 1.640060 1.641821
## [19,] 1.639356 1.641322 1.643288 1.645255 1.647221 1.649188 1.651154 1.653121
## [20,] 1.649215 1.651388 1.653560 1.655732 1.657904 1.660076 1.662248 1.664420
## [21,] 1.659075 1.661453 1.663831 1.666209 1.668587 1.670964 1.673342 1.675720
## [22,] 1.668935 1.671518 1.674102 1.676686 1.679269 1.681853 1.684436 1.687020
## [23,] 1.678795 1.681584 1.684373 1.687162 1.689952 1.692741 1.695530 1.698319
## [24,] 1.688654 1.691649 1.694644 1.697639 1.700634 1.703629 1.706624 1.709619
## [25,] 1.698514 1.701715 1.704916 1.708116 1.711317 1.714518 1.717718 1.720919
## [26,] 1.708374 1.711780 1.715187 1.718593 1.722000 1.725406 1.728812 1.732219
## [27,] 1.718234 1.721846 1.725458 1.729070 1.732682 1.736294 1.739906 1.743518
## [28,] 1.728093 1.731911 1.735729 1.739547 1.743365 1.747183 1.751000 1.754818
## [29,] 1.737953 1.741977 1.746000 1.750024 1.754047 1.758071 1.762094 1.766118
## [30,] 1.747813 1.752042 1.756271 1.760501 1.764730 1.768959 1.773188 1.777418
## [31,] 1.757673 1.762108 1.766543 1.770978 1.775413 1.779847 1.784282 1.788717
## [32,] 1.767533 1.772173 1.776814 1.781454 1.786095 1.790736 1.795376 1.800017
## [33,] 1.777392 1.782239 1.787085 1.791931 1.796778 1.801624 1.806470 1.811317
## [34,] 1.787252 1.792304 1.797356 1.802408 1.807460 1.812512 1.817564 1.822617
## [35,] 1.797112 1.802370 1.807627 1.812885 1.818143 1.823401 1.828658 1.833916
## [36,] 1.806972 1.812435 1.817899 1.823362 1.828826 1.834289 1.839753 1.845216
## [37,] 1.816831 1.822501 1.828170 1.833839 1.839508 1.845177 1.850847 1.856516
## [38,] 1.826691 1.832566 1.838441 1.844316 1.850191 1.856066 1.861941 1.867815
## [39,] 1.836551 1.842631 1.848712 1.854793 1.860873 1.866954 1.873035 1.879115
## [40,] 1.846411 1.852697 1.858983 1.865270 1.871556 1.877842 1.884129 1.890415
## [41,] 1.856270 1.862762 1.869254 1.875747 1.882239 1.888731 1.895223 1.901715
## [42,] 1.866130 1.872828 1.879526 1.886223 1.892921 1.899619 1.906317 1.913014
## [43,] 1.875990 1.882893 1.889797 1.896700 1.903604 1.910507 1.917411 1.924314
## [44,] 1.885850 1.892959 1.900068 1.907177 1.914286 1.921396 1.928505 1.935614
## [45,] 1.895709 1.903024 1.910339 1.917654 1.924969 1.932284 1.939599 1.946914
## [46,] 1.905569 1.913090 1.920610 1.928131 1.935652 1.943172 1.950693 1.958213
## [47,] 1.915429 1.923155 1.930882 1.938608 1.946334 1.954060 1.961787 1.969513
## [48,] 1.925289 1.933221 1.941153 1.949085 1.957017 1.964949 1.972881 1.980813
## [49,] 1.935148 1.943286 1.951424 1.959562 1.967699 1.975837 1.983975 1.992113
## [50,] 1.945008 1.953352 1.961695 1.970039 1.978382 1.986725 1.995069 2.003412
## [51,] 1.954868 1.963417 1.971966 1.980515 1.989065 1.997614 2.006163 2.014712
## [52,] 1.964728 1.973483 1.982237 1.990992 1.999747 2.008502 2.017257 2.026012
## [53,] 1.974588 1.983548 1.992509 2.001469 2.010430 2.019390 2.028351 2.037311
## [54,] 1.984447 1.993614 2.002780 2.011946 2.021112 2.030279 2.039445 2.048611
## [55,] 1.994307 2.003679 2.013051 2.022423 2.031795 2.041167 2.050539 2.059911
## [56,] 2.004167 2.013744 2.023322 2.032900 2.042478 2.052055 2.061633 2.071211
## [57,] 2.014027 2.023810 2.033593 2.043377 2.053160 2.062944 2.072727 2.082510
## [58,] 2.023886 2.033875 2.043865 2.053854 2.063843 2.073832 2.083821 2.093810
## [59,] 2.033746 2.043941 2.054136 2.064331 2.074525 2.084720 2.094915 2.105110
## [60,] 2.043606 2.054006 2.064407 2.074807 2.085208 2.095609 2.106009 2.116410
## [61,] 2.053466 2.064072 2.074678 2.085284 2.095891 2.106497 2.117103 2.127709
## [62,] 2.063325 2.074137 2.084949 2.095761 2.106573 2.117385 2.128197 2.139009
## [63,] 2.073185 2.084203 2.095220 2.106238 2.117256 2.128273 2.139291 2.150309
## [64,] 2.083045 2.094268 2.105492 2.116715 2.127938 2.139162 2.150385 2.161609
## [65,] 2.092905 2.104334 2.115763 2.127192 2.138621 2.150050 2.161479 2.172908
## [66,] 2.102764 2.114399 2.126034 2.137669 2.149304 2.160938 2.172573 2.184208
## [67,] 2.112624 2.124465 2.136305 2.148146 2.159986 2.171827 2.183667 2.195508
## [68,] 2.122484 2.134530 2.146576 2.158623 2.170669 2.182715 2.194761 2.206807
## [69,] 2.132344 2.144596 2.156848 2.169099 2.181351 2.193603 2.205855 2.218107
## [70,] 2.142203 2.154661 2.167119 2.179576 2.192034 2.204492 2.216949 2.229407
## [71,] 2.152063 2.164727 2.177390 2.190053 2.202717 2.215380 2.228043 2.240707
## [72,] 2.161923 2.174792 2.187661 2.200530 2.213399 2.226268 2.239137 2.252006
## [73,] 2.171783 2.184857 2.197932 2.211007 2.224082 2.237157 2.250231 2.263306
## [74,] 2.181642 2.194923 2.208203 2.221484 2.234764 2.248045 2.261325 2.274606
## [75,] 2.191502 2.204988 2.218475 2.231961 2.245447 2.258933 2.272419 2.285906
## [76,] 2.201362 2.215054 2.228746 2.242438 2.256130 2.269821 2.283513 2.297205
## [77,] 2.211222 2.225119 2.239017 2.252915 2.266812 2.280710 2.294607 2.308505
## [78,] 2.221082 2.235185 2.249288 2.263391 2.277495 2.291598 2.305701 2.319805
## [79,] 2.230941 2.245250 2.259559 2.273868 2.288177 2.302486 2.316795 2.331104
## [80,] 2.240801 2.255316 2.269831 2.284345 2.298860 2.313375 2.327889 2.342404
## [81,] 2.250661 2.265381 2.280102 2.294822 2.309543 2.324263 2.338984 2.353704
## [82,] 2.260521 2.275447 2.290373 2.305299 2.320225 2.335151 2.350078 2.365004
## [83,] 2.270380 2.285512 2.300644 2.315776 2.330908 2.346040 2.361172 2.376303
## [84,] 2.280240 2.295578 2.310915 2.326253 2.341590 2.356928 2.372266 2.387603
## [85,] 2.290100 2.305643 2.321186 2.336730 2.352273 2.367816 2.383360 2.398903
## [86,] 2.299960 2.315709 2.331458 2.347207 2.362956 2.378705 2.394454 2.410203
## [87,] 2.309819 2.325774 2.341729 2.357683 2.373638 2.389593 2.405548 2.421502
## [88,] 2.319679 2.335840 2.352000 2.368160 2.384321 2.400481 2.416642 2.432802
## [89,] 2.329539 2.345905 2.362271 2.378637 2.395003 2.411370 2.427736 2.444102
## [90,] 2.339399 2.355970 2.372542 2.389114 2.405686 2.422258 2.438830 2.455402
## [91,] 2.349258 2.366036 2.382814 2.399591 2.416369 2.433146 2.449924 2.466701
## [92,] 2.359118 2.376101 2.393085 2.410068 2.427051 2.444034 2.461018 2.478001
## [93,] 2.368978 2.386167 2.403356 2.420545 2.437734 2.454923 2.472112 2.489301
## [94,] 2.378838 2.396232 2.413627 2.431022 2.448416 2.465811 2.483206 2.500600
## [95,] 2.388697 2.406298 2.423898 2.441499 2.459099 2.476699 2.494300 2.511900
## [96,] 2.398557 2.416363 2.434169 2.451976 2.469782 2.487588 2.505394 2.523200
## [97,] 2.408417 2.426429 2.444441 2.462452 2.480464 2.498476 2.516488 2.534500
## [98,] 2.418277 2.436494 2.454712 2.472929 2.491147 2.509364 2.527582 2.545799
## [99,] 2.428136 2.446560 2.464983 2.483406 2.501829 2.520253 2.538676 2.557099
## [,81] [,82] [,83] [,84] [,85] [,86] [,87] [,88]
## [1,] 1.447989 1.446253 1.444516 1.442780 1.441044 1.439307 1.437571 1.435834
## [2,] 1.459494 1.457964 1.456433 1.454902 1.453372 1.451841 1.450310 1.448780
## [3,] 1.471000 1.469675 1.468350 1.467025 1.465700 1.464375 1.463050 1.461725
## [4,] 1.482505 1.481386 1.480267 1.479148 1.478028 1.476909 1.475790 1.474671
## [5,] 1.494011 1.493097 1.492184 1.491270 1.490357 1.489443 1.488530 1.487616
## [6,] 1.505516 1.504808 1.504101 1.503393 1.502685 1.501977 1.501269 1.500561
## [7,] 1.517022 1.516520 1.516017 1.515515 1.515013 1.514511 1.514009 1.513507
## [8,] 1.528527 1.528231 1.527934 1.527638 1.527342 1.527045 1.526749 1.526452
## [9,] 1.540033 1.539942 1.539851 1.539760 1.539670 1.539579 1.539488 1.539398
## [10,] 1.551538 1.551653 1.551768 1.551883 1.551998 1.552113 1.552228 1.552343
## [11,] 1.563043 1.563364 1.563685 1.564006 1.564326 1.564647 1.564968 1.565289
## [12,] 1.574549 1.575075 1.575602 1.576128 1.576655 1.577181 1.577708 1.578234
## [13,] 1.586054 1.586786 1.587519 1.588251 1.588983 1.589715 1.590447 1.591179
## [14,] 1.597560 1.598498 1.599435 1.600373 1.601311 1.602249 1.603187 1.604125
## [15,] 1.609065 1.610209 1.611352 1.612496 1.613639 1.614783 1.615927 1.617070
## [16,] 1.620571 1.621920 1.623269 1.624618 1.625968 1.627317 1.628666 1.630016
## [17,] 1.632076 1.633631 1.635186 1.636741 1.638296 1.639851 1.641406 1.642961
## [18,] 1.643582 1.645342 1.647103 1.648864 1.650624 1.652385 1.654146 1.655906
## [19,] 1.655087 1.657053 1.659020 1.660986 1.662953 1.664919 1.666885 1.668852
## [20,] 1.666592 1.668765 1.670937 1.673109 1.675281 1.677453 1.679625 1.681797
## [21,] 1.678098 1.680476 1.682854 1.685231 1.687609 1.689987 1.692365 1.694743
## [22,] 1.689603 1.692187 1.694770 1.697354 1.699937 1.702521 1.705105 1.707688
## [23,] 1.701109 1.703898 1.706687 1.709477 1.712266 1.715055 1.717844 1.720634
## [24,] 1.712614 1.715609 1.718604 1.721599 1.724594 1.727589 1.730584 1.733579
## [25,] 1.724120 1.727320 1.730521 1.733722 1.736922 1.740123 1.743324 1.746524
## [26,] 1.735625 1.739031 1.742438 1.745844 1.749251 1.752657 1.756063 1.759470
## [27,] 1.747131 1.750743 1.754355 1.757967 1.761579 1.765191 1.768803 1.772415
## [28,] 1.758636 1.762454 1.766272 1.770089 1.773907 1.777725 1.781543 1.785361
## [29,] 1.770141 1.774165 1.778188 1.782212 1.786235 1.790259 1.794282 1.798306
## [30,] 1.781647 1.785876 1.790105 1.794335 1.798564 1.802793 1.807022 1.811251
## [31,] 1.793152 1.797587 1.802022 1.806457 1.810892 1.815327 1.819762 1.824197
## [32,] 1.804658 1.809298 1.813939 1.818580 1.823220 1.827861 1.832502 1.837142
## [33,] 1.816163 1.821010 1.825856 1.830702 1.835549 1.840395 1.845241 1.850088
## [34,] 1.827669 1.832721 1.837773 1.842825 1.847877 1.852929 1.857981 1.863033
## [35,] 1.839174 1.844432 1.849690 1.854947 1.860205 1.865463 1.870721 1.875979
## [36,] 1.850679 1.856143 1.861606 1.867070 1.872533 1.877997 1.883460 1.888924
## [37,] 1.862185 1.867854 1.873523 1.879193 1.884862 1.890531 1.896200 1.901869
## [38,] 1.873690 1.879565 1.885440 1.891315 1.897190 1.903065 1.908940 1.914815
## [39,] 1.885196 1.891276 1.897357 1.903438 1.909518 1.915599 1.921680 1.927760
## [40,] 1.896701 1.902988 1.909274 1.915560 1.921847 1.928133 1.934419 1.940706
## [41,] 1.908207 1.914699 1.921191 1.927683 1.934175 1.940667 1.947159 1.953651
## [42,] 1.919712 1.926410 1.933108 1.939805 1.946503 1.953201 1.959899 1.966596
## [43,] 1.931218 1.938121 1.945025 1.951928 1.958831 1.965735 1.972638 1.979542
## [44,] 1.942723 1.949832 1.956941 1.964051 1.971160 1.978269 1.985378 1.992487
## [45,] 1.954228 1.961543 1.968858 1.976173 1.983488 1.990803 1.998118 2.005433
## [46,] 1.965734 1.973255 1.980775 1.988296 1.995816 2.003337 2.010857 2.018378
## [47,] 1.977239 1.984966 1.992692 2.000418 2.008145 2.015871 2.023597 2.031323
## [48,] 1.988745 1.996677 2.004609 2.012541 2.020473 2.028405 2.036337 2.044269
## [49,] 2.000250 2.008388 2.016526 2.024663 2.032801 2.040939 2.049077 2.057214
## [50,] 2.011756 2.020099 2.028443 2.036786 2.045129 2.053473 2.061816 2.070160
## [51,] 2.023261 2.031810 2.040359 2.048909 2.057458 2.066007 2.074556 2.083105
## [52,] 2.034767 2.043521 2.052276 2.061031 2.069786 2.078541 2.087296 2.096051
## [53,] 2.046272 2.055233 2.064193 2.073154 2.082114 2.091075 2.100035 2.108996
## [54,] 2.057777 2.066944 2.076110 2.085276 2.094443 2.103609 2.112775 2.121941
## [55,] 2.069283 2.078655 2.088027 2.097399 2.106771 2.116143 2.125515 2.134887
## [56,] 2.080788 2.090366 2.099944 2.109521 2.119099 2.128677 2.138255 2.147832
## [57,] 2.092294 2.102077 2.111861 2.121644 2.131427 2.141211 2.150994 2.160778
## [58,] 2.103799 2.113788 2.123777 2.133767 2.143756 2.153745 2.163734 2.173723
## [59,] 2.115305 2.125499 2.135694 2.145889 2.156084 2.166279 2.176474 2.186668
## [60,] 2.126810 2.137211 2.147611 2.158012 2.168412 2.178813 2.189213 2.199614
## [61,] 2.138316 2.148922 2.159528 2.170134 2.180741 2.191347 2.201953 2.212559
## [62,] 2.149821 2.160633 2.171445 2.182257 2.193069 2.203881 2.214693 2.225505
## [63,] 2.161326 2.172344 2.183362 2.194379 2.205397 2.216415 2.227432 2.238450
## [64,] 2.172832 2.184055 2.195279 2.206502 2.217725 2.228949 2.240172 2.251396
## [65,] 2.184337 2.195766 2.207195 2.218625 2.230054 2.241483 2.252912 2.264341
## [66,] 2.195843 2.207478 2.219112 2.230747 2.242382 2.254017 2.265652 2.277286
## [67,] 2.207348 2.219189 2.231029 2.242870 2.254710 2.266551 2.278391 2.290232
## [68,] 2.218854 2.230900 2.242946 2.254992 2.267039 2.279085 2.291131 2.303177
## [69,] 2.230359 2.242611 2.254863 2.267115 2.279367 2.291619 2.303871 2.316123
## [70,] 2.241865 2.254322 2.266780 2.279237 2.291695 2.304153 2.316610 2.329068
## [71,] 2.253370 2.266033 2.278697 2.291360 2.304023 2.316687 2.329350 2.342013
## [72,] 2.264875 2.277744 2.290614 2.303483 2.316352 2.329221 2.342090 2.354959
## [73,] 2.276381 2.289456 2.302530 2.315605 2.328680 2.341755 2.354829 2.367904
## [74,] 2.287886 2.301167 2.314447 2.327728 2.341008 2.354289 2.367569 2.380850
## [75,] 2.299392 2.312878 2.326364 2.339850 2.353337 2.366823 2.380309 2.393795
## [76,] 2.310897 2.324589 2.338281 2.351973 2.365665 2.379357 2.393049 2.406740
## [77,] 2.322403 2.336300 2.350198 2.364095 2.377993 2.391891 2.405788 2.419686
## [78,] 2.333908 2.348011 2.362115 2.376218 2.390321 2.404425 2.418528 2.432631
## [79,] 2.345414 2.359723 2.374032 2.388341 2.402650 2.416959 2.431268 2.445577
## [80,] 2.356919 2.371434 2.385948 2.400463 2.414978 2.429493 2.444007 2.458522
## [81,] 2.368424 2.383145 2.397865 2.412586 2.427306 2.442027 2.456747 2.471468
## [82,] 2.379930 2.394856 2.409782 2.424708 2.439634 2.454561 2.469487 2.484413
## [83,] 2.391435 2.406567 2.421699 2.436831 2.451963 2.467095 2.482227 2.497358
## [84,] 2.402941 2.418278 2.433616 2.448953 2.464291 2.479629 2.494966 2.510304
## [85,] 2.414446 2.429989 2.445533 2.461076 2.476619 2.492163 2.507706 2.523249
## [86,] 2.425952 2.441701 2.457450 2.473199 2.488948 2.504697 2.520446 2.536195
## [87,] 2.437457 2.453412 2.469366 2.485321 2.501276 2.517231 2.533185 2.549140
## [88,] 2.448963 2.465123 2.481283 2.497444 2.513604 2.529765 2.545925 2.562085
## [89,] 2.460468 2.476834 2.493200 2.509566 2.525932 2.542299 2.558665 2.575031
## [90,] 2.471973 2.488545 2.505117 2.521689 2.538261 2.554833 2.571404 2.587976
## [91,] 2.483479 2.500256 2.517034 2.533811 2.550589 2.567367 2.584144 2.600922
## [92,] 2.494984 2.511968 2.528951 2.545934 2.562917 2.579901 2.596884 2.613867
## [93,] 2.506490 2.523679 2.540868 2.558057 2.575246 2.592435 2.609624 2.626813
## [94,] 2.517995 2.535390 2.552785 2.570179 2.587574 2.604969 2.622363 2.639758
## [95,] 2.529501 2.547101 2.564701 2.582302 2.599902 2.617503 2.635103 2.652703
## [96,] 2.541006 2.558812 2.576618 2.594424 2.612230 2.630037 2.647843 2.665649
## [97,] 2.552511 2.570523 2.588535 2.606547 2.624559 2.642571 2.660582 2.678594
## [98,] 2.564017 2.582234 2.600452 2.618670 2.636887 2.655105 2.673322 2.691540
## [99,] 2.575522 2.593946 2.612369 2.630792 2.649215 2.667639 2.686062 2.704485
## [,89] [,90] [,91] [,92] [,93] [,94] [,95] [,96]
## [1,] 1.434098 1.432362 1.430625 1.428889 1.427153 1.425416 1.423680 1.421943
## [2,] 1.447249 1.445719 1.444188 1.442657 1.441127 1.439596 1.438065 1.436535
## [3,] 1.460400 1.459075 1.457750 1.456425 1.455100 1.453776 1.452451 1.451126
## [4,] 1.473551 1.472432 1.471313 1.470194 1.469074 1.467955 1.466836 1.465717
## [5,] 1.486703 1.485789 1.484875 1.483962 1.483048 1.482135 1.481221 1.480308
## [6,] 1.499854 1.499146 1.498438 1.497730 1.497022 1.496315 1.495607 1.494899
## [7,] 1.513005 1.512503 1.512001 1.511498 1.510996 1.510494 1.509992 1.509490
## [8,] 1.526156 1.525860 1.525563 1.525267 1.524970 1.524674 1.524378 1.524081
## [9,] 1.539307 1.539216 1.539126 1.539035 1.538944 1.538854 1.538763 1.538672
## [10,] 1.552458 1.552573 1.552688 1.552803 1.552918 1.553033 1.553148 1.553263
## [11,] 1.565609 1.565930 1.566251 1.566571 1.566892 1.567213 1.567534 1.567854
## [12,] 1.578760 1.579287 1.579813 1.580340 1.580866 1.581393 1.581919 1.582446
## [13,] 1.591912 1.592644 1.593376 1.594108 1.594840 1.595572 1.596304 1.597037
## [14,] 1.605063 1.606001 1.606938 1.607876 1.608814 1.609752 1.610690 1.611628
## [15,] 1.618214 1.619357 1.620501 1.621645 1.622788 1.623932 1.625075 1.626219
## [16,] 1.631365 1.632714 1.634063 1.635413 1.636762 1.638111 1.639461 1.640810
## [17,] 1.644516 1.646071 1.647626 1.649181 1.650736 1.652291 1.653846 1.655401
## [18,] 1.657667 1.659428 1.661189 1.662949 1.664710 1.666471 1.668231 1.669992
## [19,] 1.670818 1.672785 1.674751 1.676718 1.678684 1.680650 1.682617 1.684583
## [20,] 1.683969 1.686142 1.688314 1.690486 1.692658 1.694830 1.697002 1.699174
## [21,] 1.697121 1.699498 1.701876 1.704254 1.706632 1.709010 1.711388 1.713765
## [22,] 1.710272 1.712855 1.715439 1.718022 1.720606 1.723189 1.725773 1.728356
## [23,] 1.723423 1.726212 1.729001 1.731791 1.734580 1.737369 1.740158 1.742948
## [24,] 1.736574 1.739569 1.742564 1.745559 1.748554 1.751549 1.754544 1.757539
## [25,] 1.749725 1.752926 1.756126 1.759327 1.762528 1.765728 1.768929 1.772130
## [26,] 1.762876 1.766283 1.769689 1.773095 1.776502 1.779908 1.783314 1.786721
## [27,] 1.776027 1.779639 1.783251 1.786864 1.790476 1.794088 1.797700 1.801312
## [28,] 1.789178 1.792996 1.796814 1.800632 1.804450 1.808267 1.812085 1.815903
## [29,] 1.802330 1.806353 1.810377 1.814400 1.818424 1.822447 1.826471 1.830494
## [30,] 1.815481 1.819710 1.823939 1.828168 1.832398 1.836627 1.840856 1.845085
## [31,] 1.828632 1.833067 1.837502 1.841937 1.846372 1.850806 1.855241 1.859676
## [32,] 1.841783 1.846424 1.851064 1.855705 1.860345 1.864986 1.869627 1.874267
## [33,] 1.854934 1.859780 1.864627 1.869473 1.874319 1.879166 1.884012 1.888859
## [34,] 1.868085 1.873137 1.878189 1.883241 1.888293 1.893345 1.898398 1.903450
## [35,] 1.881236 1.886494 1.891752 1.897010 1.902267 1.907525 1.912783 1.918041
## [36,] 1.894387 1.899851 1.905314 1.910778 1.916241 1.921705 1.927168 1.932632
## [37,] 1.907539 1.913208 1.918877 1.924546 1.930215 1.935885 1.941554 1.947223
## [38,] 1.920690 1.926565 1.932439 1.938314 1.944189 1.950064 1.955939 1.961814
## [39,] 1.933841 1.939921 1.946002 1.952083 1.958163 1.964244 1.970324 1.976405
## [40,] 1.946992 1.953278 1.959565 1.965851 1.972137 1.978424 1.984710 1.990996
## [41,] 1.960143 1.966635 1.973127 1.979619 1.986111 1.992603 1.999095 2.005587
## [42,] 1.973294 1.979992 1.986690 1.993387 2.000085 2.006783 2.013481 2.020178
## [43,] 1.986445 1.993349 2.000252 2.007156 2.014059 2.020963 2.027866 2.034770
## [44,] 1.999596 2.006706 2.013815 2.020924 2.028033 2.035142 2.042251 2.049361
## [45,] 2.012748 2.020062 2.027377 2.034692 2.042007 2.049322 2.056637 2.063952
## [46,] 2.025899 2.033419 2.040940 2.048460 2.055981 2.063502 2.071022 2.078543
## [47,] 2.039050 2.046776 2.054502 2.062229 2.069955 2.077681 2.085408 2.093134
## [48,] 2.052201 2.060133 2.068065 2.075997 2.083929 2.091861 2.099793 2.107725
## [49,] 2.065352 2.073490 2.081627 2.089765 2.097903 2.106041 2.114178 2.122316
## [50,] 2.078503 2.086847 2.095190 2.103533 2.111877 2.120220 2.128564 2.136907
## [51,] 2.091654 2.100203 2.108753 2.117302 2.125851 2.134400 2.142949 2.151498
## [52,] 2.104805 2.113560 2.122315 2.131070 2.139825 2.148580 2.157335 2.166089
## [53,] 2.117957 2.126917 2.135878 2.144838 2.153799 2.162759 2.171720 2.180680
## [54,] 2.131108 2.140274 2.149440 2.158606 2.167773 2.176939 2.186105 2.195272
## [55,] 2.144259 2.153631 2.163003 2.172375 2.181747 2.191119 2.200491 2.209863
## [56,] 2.157410 2.166988 2.176565 2.186143 2.195721 2.205298 2.214876 2.224454
## [57,] 2.170561 2.180344 2.190128 2.199911 2.209695 2.219478 2.229261 2.239045
## [58,] 2.183712 2.193701 2.203690 2.213679 2.223669 2.233658 2.243647 2.253636
## [59,] 2.196863 2.207058 2.217253 2.227448 2.237643 2.247837 2.258032 2.268227
## [60,] 2.210014 2.220415 2.230815 2.241216 2.251617 2.262017 2.272418 2.282818
## [61,] 2.223166 2.233772 2.244378 2.254984 2.265591 2.276197 2.286803 2.297409
## [62,] 2.236317 2.247129 2.257941 2.268753 2.279564 2.290376 2.301188 2.312000
## [63,] 2.249468 2.260485 2.271503 2.282521 2.293538 2.304556 2.315574 2.326591
## [64,] 2.262619 2.273842 2.285066 2.296289 2.307512 2.318736 2.329959 2.341183
## [65,] 2.275770 2.287199 2.298628 2.310057 2.321486 2.332915 2.344345 2.355774
## [66,] 2.288921 2.300556 2.312191 2.323826 2.335460 2.347095 2.358730 2.370365
## [67,] 2.302072 2.313913 2.325753 2.337594 2.349434 2.361275 2.373115 2.384956
## [68,] 2.315223 2.327270 2.339316 2.351362 2.363408 2.375454 2.387501 2.399547
## [69,] 2.328375 2.340626 2.352878 2.365130 2.377382 2.389634 2.401886 2.414138
## [70,] 2.341526 2.353983 2.366441 2.378899 2.391356 2.403814 2.416271 2.428729
## [71,] 2.354677 2.367340 2.380003 2.392667 2.405330 2.417994 2.430657 2.443320
## [72,] 2.367828 2.380697 2.393566 2.406435 2.419304 2.432173 2.445042 2.457911
## [73,] 2.380979 2.394054 2.407129 2.420203 2.433278 2.446353 2.459428 2.472502
## [74,] 2.394130 2.407411 2.420691 2.433972 2.447252 2.460533 2.473813 2.487093
## [75,] 2.407281 2.420767 2.434254 2.447740 2.461226 2.474712 2.488198 2.501685
## [76,] 2.420432 2.434124 2.447816 2.461508 2.475200 2.488892 2.502584 2.516276
## [77,] 2.433584 2.447481 2.461379 2.475276 2.489174 2.503072 2.516969 2.530867
## [78,] 2.446735 2.460838 2.474941 2.489045 2.503148 2.517251 2.531355 2.545458
## [79,] 2.459886 2.474195 2.488504 2.502813 2.517122 2.531431 2.545740 2.560049
## [80,] 2.473037 2.487552 2.502066 2.516581 2.531096 2.545611 2.560125 2.574640
## [81,] 2.486188 2.500908 2.515629 2.530349 2.545070 2.559790 2.574511 2.589231
## [82,] 2.499339 2.514265 2.529191 2.544118 2.559044 2.573970 2.588896 2.603822
## [83,] 2.512490 2.527622 2.542754 2.557886 2.573018 2.588150 2.603281 2.618413
## [84,] 2.525641 2.540979 2.556317 2.571654 2.586992 2.602329 2.617667 2.633004
## [85,] 2.538793 2.554336 2.569879 2.585422 2.600966 2.616509 2.632052 2.647596
## [86,] 2.551944 2.567693 2.583442 2.599191 2.614940 2.630689 2.646438 2.662187
## [87,] 2.565095 2.581049 2.597004 2.612959 2.628914 2.644868 2.660823 2.676778
## [88,] 2.578246 2.594406 2.610567 2.626727 2.642888 2.659048 2.675208 2.691369
## [89,] 2.591397 2.607763 2.624129 2.640495 2.656862 2.673228 2.689594 2.705960
## [90,] 2.604548 2.621120 2.637692 2.654264 2.670836 2.687407 2.703979 2.720551
## [91,] 2.617699 2.634477 2.651254 2.668032 2.684809 2.701587 2.718365 2.735142
## [92,] 2.630850 2.647834 2.664817 2.681800 2.698783 2.715767 2.732750 2.749733
## [93,] 2.644002 2.661190 2.678379 2.695568 2.712757 2.729946 2.747135 2.764324
## [94,] 2.657153 2.674547 2.691942 2.709337 2.726731 2.744126 2.761521 2.778915
## [95,] 2.670304 2.687904 2.705505 2.723105 2.740705 2.758306 2.775906 2.793507
## [96,] 2.683455 2.701261 2.719067 2.736873 2.754679 2.772485 2.790292 2.808098
## [97,] 2.696606 2.714618 2.732630 2.750641 2.768653 2.786665 2.804677 2.822689
## [98,] 2.709757 2.727975 2.746192 2.764410 2.782627 2.800845 2.819062 2.837280
## [99,] 2.722908 2.741331 2.759755 2.778178 2.796601 2.815024 2.833448 2.851871
## [,97] [,98] [,99]
## [1,] 1.420207 1.418471 1.416734
## [2,] 1.435004 1.433473 1.431943
## [3,] 1.449801 1.448476 1.447151
## [4,] 1.464597 1.463478 1.462359
## [5,] 1.479394 1.478481 1.477567
## [6,] 1.494191 1.493483 1.492775
## [7,] 1.508988 1.508486 1.507984
## [8,] 1.523785 1.523488 1.523192
## [9,] 1.538582 1.538491 1.538400
## [10,] 1.553378 1.553493 1.553608
## [11,] 1.568175 1.568496 1.568817
## [12,] 1.582972 1.583498 1.584025
## [13,] 1.597769 1.598501 1.599233
## [14,] 1.612566 1.613503 1.614441
## [15,] 1.627362 1.628506 1.629650
## [16,] 1.642159 1.643508 1.644858
## [17,] 1.656956 1.658511 1.660066
## [18,] 1.671753 1.673513 1.675274
## [19,] 1.686550 1.688516 1.690482
## [20,] 1.701346 1.703519 1.705691
## [21,] 1.716143 1.718521 1.720899
## [22,] 1.730940 1.733524 1.736107
## [23,] 1.745737 1.748526 1.751315
## [24,] 1.760534 1.763529 1.766524
## [25,] 1.775330 1.778531 1.781732
## [26,] 1.790127 1.793534 1.796940
## [27,] 1.804924 1.808536 1.812148
## [28,] 1.819721 1.823539 1.827356
## [29,] 1.834518 1.838541 1.842565
## [30,] 1.849314 1.853544 1.857773
## [31,] 1.864111 1.868546 1.872981
## [32,] 1.878908 1.883549 1.888189
## [33,] 1.893705 1.898551 1.903398
## [34,] 1.908502 1.913554 1.918606
## [35,] 1.923299 1.928556 1.933814
## [36,] 1.938095 1.943559 1.949022
## [37,] 1.952892 1.958561 1.964231
## [38,] 1.967689 1.973564 1.979439
## [39,] 1.982486 1.988566 1.994647
## [40,] 1.997283 2.003569 2.009855
## [41,] 2.012079 2.018571 2.025063
## [42,] 2.026876 2.033574 2.040272
## [43,] 2.041673 2.048576 2.055480
## [44,] 2.056470 2.063579 2.070688
## [45,] 2.071267 2.078581 2.085896
## [46,] 2.086063 2.093584 2.101105
## [47,] 2.100860 2.108586 2.116313
## [48,] 2.115657 2.123589 2.131521
## [49,] 2.130454 2.138592 2.146729
## [50,] 2.145251 2.153594 2.161937
## [51,] 2.160047 2.168597 2.177146
## [52,] 2.174844 2.183599 2.192354
## [53,] 2.189641 2.198602 2.207562
## [54,] 2.204438 2.213604 2.222770
## [55,] 2.219235 2.228607 2.237979
## [56,] 2.234031 2.243609 2.253187
## [57,] 2.248828 2.258612 2.268395
## [58,] 2.263625 2.273614 2.283603
## [59,] 2.278422 2.288617 2.298812
## [60,] 2.293219 2.303619 2.314020
## [61,] 2.308015 2.318622 2.329228
## [62,] 2.322812 2.333624 2.344436
## [63,] 2.337609 2.348627 2.359644
## [64,] 2.352406 2.363629 2.374853
## [65,] 2.367203 2.378632 2.390061
## [66,] 2.382000 2.393634 2.405269
## [67,] 2.396796 2.408637 2.420477
## [68,] 2.411593 2.423639 2.435686
## [69,] 2.426390 2.438642 2.450894
## [70,] 2.441187 2.453644 2.466102
## [71,] 2.455984 2.468647 2.481310
## [72,] 2.470780 2.483649 2.496518
## [73,] 2.485577 2.498652 2.511727
## [74,] 2.500374 2.513654 2.526935
## [75,] 2.515171 2.528657 2.542143
## [76,] 2.529968 2.543659 2.557351
## [77,] 2.544764 2.558662 2.572560
## [78,] 2.559561 2.573665 2.587768
## [79,] 2.574358 2.588667 2.602976
## [80,] 2.589155 2.603670 2.618184
## [81,] 2.603952 2.618672 2.633393
## [82,] 2.618748 2.633675 2.648601
## [83,] 2.633545 2.648677 2.663809
## [84,] 2.648342 2.663680 2.679017
## [85,] 2.663139 2.678682 2.694225
## [86,] 2.677936 2.693685 2.709434
## [87,] 2.692732 2.708687 2.724642
## [88,] 2.707529 2.723690 2.739850
## [89,] 2.722326 2.738692 2.755058
## [90,] 2.737123 2.753695 2.770267
## [91,] 2.751920 2.768697 2.785475
## [92,] 2.766716 2.783700 2.800683
## [93,] 2.781513 2.798702 2.815891
## [94,] 2.796310 2.813705 2.831099
## [95,] 2.811107 2.828707 2.846308
## [96,] 2.825904 2.843710 2.861516
## [97,] 2.840701 2.858712 2.876724
## [98,] 2.855497 2.873715 2.891932
## [99,] 2.870294 2.888717 2.907141
##
## $meta
## $meta$x
## [1] "Pre_Pene_AVG"
##
## $meta$y
## [1] "Density_Num"
##
## $meta$trans
## function (x)
## {
## structure(x, class = unique(c("AsIs", oldClass(x))))
## }
## <bytecode: 0x7ffd25ad3018>
## <environment: namespace:base>
##
## $meta$class
## [1] "negbin" "glm" "lm"
##
## $meta$cond
## Site Year_Fac
## 1 0.5 0.5
##
##
## attr(,"class")
## [1] "visreg2d"show(VRB_2)## $x
## [1] 0.000000 0.377551 0.755102 1.132653 1.510204 1.887755 2.265306
## [8] 2.642857 3.020408 3.397959 3.775510 4.153061 4.530612 4.908163
## [15] 5.285714 5.663265 6.040816 6.418367 6.795918 7.173469 7.551020
## [22] 7.928571 8.306122 8.683673 9.061224 9.438776 9.816327 10.193878
## [29] 10.571429 10.948980 11.326531 11.704082 12.081633 12.459184 12.836735
## [36] 13.214286 13.591837 13.969388 14.346939 14.724490 15.102041 15.479592
## [43] 15.857143 16.234694 16.612245 16.989796 17.367347 17.744898 18.122449
## [50] 18.500000 18.877551 19.255102 19.632653 20.010204 20.387755 20.765306
## [57] 21.142857 21.520408 21.897959 22.275510 22.653061 23.030612 23.408163
## [64] 23.785714 24.163265 24.540816 24.918367 25.295918 25.673469 26.051020
## [71] 26.428571 26.806122 27.183673 27.561224 27.938776 28.316327 28.693878
## [78] 29.071429 29.448980 29.826531 30.204082 30.581633 30.959184 31.336735
## [85] 31.714286 32.091837 32.469388 32.846939 33.224490 33.602041 33.979592
## [92] 34.357143 34.734694 35.112245 35.489796 35.867347 36.244898 36.622449
## [99] 37.000000
##
## $y
## [1] 0.0000000 0.2040816 0.4081633 0.6122449 0.8163265 1.0204082
## [7] 1.2244898 1.4285714 1.6326531 1.8367347 2.0408163 2.2448980
## [13] 2.4489796 2.6530612 2.8571429 3.0612245 3.2653061 3.4693878
## [19] 3.6734694 3.8775510 4.0816327 4.2857143 4.4897959 4.6938776
## [25] 4.8979592 5.1020408 5.3061224 5.5102041 5.7142857 5.9183673
## [31] 6.1224490 6.3265306 6.5306122 6.7346939 6.9387755 7.1428571
## [37] 7.3469388 7.5510204 7.7551020 7.9591837 8.1632653 8.3673469
## [43] 8.5714286 8.7755102 8.9795918 9.1836735 9.3877551 9.5918367
## [49] 9.7959184 10.0000000 10.2040816 10.4081633 10.6122449 10.8163265
## [55] 11.0204082 11.2244898 11.4285714 11.6326531 11.8367347 12.0408163
## [61] 12.2448980 12.4489796 12.6530612 12.8571429 13.0612245 13.2653061
## [67] 13.4693878 13.6734694 13.8775510 14.0816327 14.2857143 14.4897959
## [73] 14.6938776 14.8979592 15.1020408 15.3061224 15.5102041 15.7142857
## [79] 15.9183673 16.1224490 16.3265306 16.5306122 16.7346939 16.9387755
## [85] 17.1428571 17.3469388 17.5510204 17.7551020 17.9591837 18.1632653
## [91] 18.3673469 18.5714286 18.7755102 18.9795918 19.1836735 19.3877551
## [97] 19.5918367 19.7959184 20.0000000
##
## $z
## [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8]
## [1,] 4.888564 4.880083 4.871617 4.863165 4.854728 4.846306 4.837898 4.829505
## [2,] 4.864419 4.856979 4.849550 4.842133 4.834727 4.827332 4.819949 4.812577
## [3,] 4.840393 4.833984 4.827583 4.821191 4.814808 4.808432 4.802066 4.795707
## [4,] 4.816485 4.811098 4.805716 4.800340 4.794970 4.789607 4.784249 4.778897
## [5,] 4.792696 4.788320 4.783948 4.779579 4.775215 4.770855 4.766498 4.762146
## [6,] 4.769024 4.765650 4.762278 4.758908 4.755541 4.752176 4.748814 4.745454
## [7,] 4.745469 4.743087 4.740706 4.738327 4.735948 4.733571 4.731195 4.728820
## [8,] 4.722031 4.720632 4.719233 4.717834 4.716436 4.715038 4.713641 4.712244
## [9,] 4.698708 4.698282 4.697856 4.697430 4.697004 4.696578 4.696152 4.695726
## [10,] 4.675501 4.676038 4.676576 4.677114 4.677652 4.678190 4.678728 4.679267
## [11,] 4.652408 4.653900 4.655393 4.656886 4.658380 4.659874 4.661369 4.662865
## [12,] 4.629429 4.631866 4.634306 4.636746 4.639188 4.641630 4.644075 4.646520
## [13,] 4.606563 4.609937 4.613314 4.616693 4.620074 4.623458 4.626844 4.630233
## [14,] 4.583811 4.588112 4.592417 4.596726 4.601039 4.605356 4.609677 4.614003
## [15,] 4.561171 4.566390 4.571615 4.576846 4.582083 4.587326 4.592575 4.597830
## [16,] 4.538643 4.544771 4.550907 4.557051 4.563204 4.569366 4.575535 4.581713
## [17,] 4.516226 4.523254 4.530293 4.537343 4.544404 4.551476 4.558559 4.565653
## [18,] 4.493919 4.501839 4.509772 4.517719 4.525681 4.533656 4.541646 4.549649
## [19,] 4.471723 4.480525 4.489344 4.498181 4.507035 4.515906 4.524795 4.533702
## [20,] 4.449637 4.459312 4.469009 4.478727 4.488466 4.498226 4.508007 4.517810
## [21,] 4.427659 4.438200 4.448766 4.459357 4.469973 4.480615 4.491282 4.501974
## [22,] 4.405790 4.417188 4.428614 4.440071 4.451557 4.463072 4.474618 4.486193
## [23,] 4.384030 4.396275 4.408554 4.420868 4.433216 4.445599 4.458016 4.470468
## [24,] 4.362376 4.375461 4.388585 4.401748 4.414951 4.428194 4.441476 4.454798
## [25,] 4.340830 4.354746 4.368706 4.382711 4.396762 4.410857 4.424997 4.439183
## [26,] 4.319390 4.334129 4.348917 4.363757 4.378647 4.393588 4.408579 4.423622
## [27,] 4.298056 4.313609 4.329218 4.344884 4.360607 4.376386 4.392223 4.408116
## [28,] 4.276827 4.293186 4.309608 4.326093 4.342641 4.359252 4.375926 4.392665
## [29,] 4.255703 4.272861 4.290087 4.307383 4.324749 4.342185 4.359691 4.377267
## [30,] 4.234684 4.252631 4.270655 4.288754 4.306931 4.325184 4.343515 4.361924
## [31,] 4.213768 4.232497 4.251310 4.270206 4.289186 4.308251 4.327400 4.346634
## [32,] 4.192956 4.212459 4.232053 4.251738 4.271515 4.291383 4.311344 4.331398
## [33,] 4.172246 4.192515 4.212883 4.233350 4.253916 4.274582 4.295348 4.316216
## [34,] 4.151639 4.172666 4.193800 4.215041 4.236390 4.257846 4.279412 4.301086
## [35,] 4.131133 4.152911 4.174804 4.196812 4.218936 4.241176 4.263534 4.286010
## [36,] 4.110729 4.133249 4.155893 4.178661 4.201553 4.224571 4.247716 4.270986
## [37,] 4.090426 4.113681 4.137068 4.160589 4.184243 4.208032 4.231956 4.256016
## [38,] 4.070222 4.094205 4.118329 4.142595 4.167004 4.191557 4.216254 4.241097
## [39,] 4.050119 4.074821 4.099674 4.124679 4.149836 4.175146 4.200611 4.226231
## [40,] 4.030115 4.055529 4.081104 4.106840 4.132738 4.158800 4.185026 4.211417
## [41,] 4.010210 4.036329 4.062618 4.089078 4.115711 4.142517 4.169498 4.196655
## [42,] 3.990403 4.017219 4.044216 4.071394 4.098754 4.126299 4.154029 4.181945
## [43,] 3.970693 3.998200 4.025897 4.053785 4.081867 4.110144 4.138616 4.167286
## [44,] 3.951082 3.979271 4.007661 4.036253 4.065050 4.094052 4.123261 4.152678
## [45,] 3.931567 3.960431 3.989507 4.018797 4.048302 4.078023 4.107963 4.138122
## [46,] 3.912148 3.941681 3.971436 4.001416 4.031623 4.062057 4.092721 4.123617
## [47,] 3.892825 3.923019 3.953447 3.984111 4.015012 4.046154 4.077537 4.109163
## [48,] 3.873598 3.904446 3.935539 3.966880 3.998470 4.030312 4.062408 4.094759
## [49,] 3.854466 3.885960 3.917712 3.949724 3.981997 4.014533 4.047336 4.080406
## [50,] 3.835428 3.867563 3.899966 3.932642 3.965591 3.998816 4.032319 4.066103
## [51,] 3.816484 3.849252 3.882301 3.915633 3.949252 3.983160 4.017358 4.051851
## [52,] 3.797634 3.831028 3.864715 3.898699 3.932981 3.967565 4.002453 4.037648
## [53,] 3.778877 3.812890 3.847209 3.881838 3.916777 3.952032 3.987603 4.023495
## [54,] 3.760213 3.794838 3.829783 3.865049 3.900640 3.936559 3.972808 4.009391
## [55,] 3.741641 3.776872 3.812435 3.848333 3.884569 3.921147 3.958068 3.995338
## [56,] 3.723160 3.758991 3.795166 3.831690 3.868565 3.905795 3.943383 3.981333
## [57,] 3.704771 3.741194 3.777975 3.815118 3.852626 3.890503 3.928752 3.967377
## [58,] 3.686473 3.723482 3.760862 3.798618 3.836753 3.875271 3.914176 3.953471
## [59,] 3.668265 3.705853 3.743827 3.782190 3.820946 3.860099 3.899653 3.939613
## [60,] 3.650146 3.688308 3.726869 3.765832 3.805203 3.844986 3.885185 3.925803
## [61,] 3.632118 3.670846 3.709987 3.749546 3.789526 3.829932 3.870770 3.912043
## [62,] 3.614178 3.653467 3.693182 3.733329 3.773913 3.814938 3.856408 3.898330
## [63,] 3.596327 3.636170 3.676453 3.717183 3.758364 3.800002 3.842100 3.884665
## [64,] 3.578565 3.618954 3.659800 3.701107 3.742880 3.785124 3.827845 3.871049
## [65,] 3.560890 3.601821 3.643222 3.685100 3.727459 3.770305 3.813643 3.857480
## [66,] 3.543302 3.584768 3.626720 3.669162 3.712102 3.755543 3.799494 3.843958
## [67,] 3.525801 3.567796 3.610292 3.653294 3.696808 3.740840 3.785397 3.830484
## [68,] 3.508387 3.550905 3.593939 3.637494 3.681577 3.726194 3.771352 3.817057
## [69,] 3.491058 3.534093 3.577659 3.621762 3.666409 3.711605 3.757359 3.803678
## [70,] 3.473815 3.517361 3.561454 3.606098 3.651303 3.697074 3.743419 3.790345
## [71,] 3.456658 3.500709 3.545321 3.590502 3.636259 3.682599 3.729530 3.777059
## [72,] 3.439585 3.484135 3.529262 3.574974 3.621278 3.668181 3.715693 3.763819
## [73,] 3.422596 3.467640 3.513276 3.559513 3.606358 3.653820 3.701907 3.750626
## [74,] 3.405691 3.451222 3.497362 3.544118 3.591500 3.639515 3.688172 3.737479
## [75,] 3.388870 3.434883 3.481520 3.528790 3.576703 3.625266 3.674488 3.724378
## [76,] 3.372132 3.418621 3.465750 3.513529 3.561967 3.611072 3.660855 3.711323
## [77,] 3.355477 3.402435 3.450051 3.498333 3.547291 3.596934 3.647272 3.698314
## [78,] 3.338904 3.386327 3.434424 3.483204 3.532676 3.582852 3.633740 3.685351
## [79,] 3.322412 3.370294 3.418867 3.468139 3.518122 3.568824 3.620258 3.672433
## [80,] 3.306002 3.354338 3.403380 3.453140 3.503627 3.554852 3.606826 3.659560
## [81,] 3.289674 3.338457 3.387964 3.438206 3.489192 3.540934 3.593444 3.646732
## [82,] 3.273425 3.322651 3.372618 3.423336 3.474816 3.527071 3.580111 3.633950
## [83,] 3.257257 3.306921 3.357341 3.408530 3.460500 3.513262 3.566828 3.621212
## [84,] 3.241169 3.291264 3.342133 3.393789 3.446243 3.499507 3.553595 3.608518
## [85,] 3.225161 3.275682 3.326995 3.379111 3.432044 3.485806 3.540410 3.595870
## [86,] 3.209231 3.260174 3.311924 3.364497 3.417904 3.472158 3.527274 3.583265
## [87,] 3.193380 3.244739 3.296923 3.349946 3.403822 3.458564 3.514187 3.570705
## [88,] 3.177608 3.229377 3.281989 3.335458 3.389798 3.445024 3.501149 3.558189
## [89,] 3.161913 3.214087 3.267122 3.321032 3.375832 3.431536 3.488159 3.545716
## [90,] 3.146296 3.198870 3.252323 3.306669 3.361924 3.418101 3.475217 3.533288
## [91,] 3.130756 3.183726 3.237591 3.292368 3.348072 3.404719 3.462323 3.520903
## [92,] 3.115293 3.168653 3.222926 3.278129 3.334278 3.391389 3.449477 3.508561
## [93,] 3.099906 3.153651 3.208327 3.263952 3.320541 3.378111 3.436679 3.496263
## [94,] 3.084595 3.138720 3.193795 3.249836 3.306860 3.364885 3.423928 3.484007
## [95,] 3.069360 3.123860 3.179328 3.235781 3.293236 3.351711 3.411225 3.471795
## [96,] 3.054200 3.109070 3.164927 3.221786 3.279668 3.338589 3.398568 3.459626
## [97,] 3.039115 3.094351 3.150590 3.207852 3.266155 3.325518 3.385959 3.447499
## [98,] 3.024104 3.079701 3.136319 3.193979 3.252699 3.312498 3.373396 3.435414
## [99,] 3.009168 3.065120 3.122113 3.180165 3.239297 3.299529 3.360880 3.423372
## [,9] [,10] [,11] [,12] [,13] [,14] [,15] [,16]
## [1,] 4.821127 4.812763 4.804413 4.796078 4.787758 4.779452 4.771160 4.762883
## [2,] 4.805216 4.797866 4.790528 4.783201 4.775885 4.768581 4.761287 4.754005
## [3,] 4.789358 4.783016 4.776683 4.770358 4.764042 4.757734 4.751435 4.745143
## [4,] 4.773552 4.768212 4.762878 4.757550 4.752228 4.746912 4.741602 4.736298
## [5,] 4.757798 4.753453 4.749113 4.744776 4.740444 4.736115 4.731791 4.727470
## [6,] 4.742096 4.738740 4.735387 4.732037 4.728689 4.725343 4.721999 4.718658
## [7,] 4.726446 4.724073 4.721702 4.719332 4.716963 4.714595 4.712228 4.709863
## [8,] 4.710847 4.709451 4.708056 4.706660 4.705266 4.703871 4.702477 4.701083
## [9,] 4.695300 4.694875 4.694449 4.694023 4.693598 4.693172 4.692746 4.692321
## [10,] 4.679805 4.680343 4.680882 4.681420 4.681958 4.682497 4.683036 4.683574
## [11,] 4.664360 4.665857 4.667353 4.668851 4.670348 4.671846 4.673345 4.674844
## [12,] 4.648967 4.651415 4.653864 4.656315 4.658767 4.661220 4.663675 4.666130
## [13,] 4.633624 4.637018 4.640414 4.643813 4.647214 4.650618 4.654024 4.657433
## [14,] 4.618332 4.622665 4.627003 4.631344 4.635690 4.640040 4.644394 4.648751
## [15,] 4.603090 4.608357 4.613630 4.618910 4.624195 4.629486 4.634783 4.640086
## [16,] 4.587899 4.594094 4.600297 4.606508 4.612728 4.618956 4.625192 4.631437
## [17,] 4.572758 4.579874 4.587001 4.594140 4.601289 4.608450 4.615621 4.622804
## [18,] 4.557667 4.565699 4.573745 4.581805 4.589879 4.597967 4.606070 4.614187
## [19,] 4.542625 4.551567 4.560526 4.569503 4.578497 4.587509 4.596539 4.605587
## [20,] 4.527634 4.537479 4.547346 4.557234 4.567143 4.577075 4.587027 4.597002
## [21,] 4.512691 4.523435 4.534203 4.544998 4.555818 4.566664 4.577536 4.588433
## [22,] 4.497798 4.509434 4.521099 4.532795 4.544521 4.556277 4.568063 4.579880
## [23,] 4.482955 4.495476 4.508033 4.520624 4.533251 4.545913 4.558611 4.571343
## [24,] 4.468160 4.481562 4.495004 4.508487 4.522010 4.535573 4.549177 4.562823
## [25,] 4.453414 4.467691 4.482013 4.496382 4.510796 4.525257 4.539764 4.554318
## [26,] 4.438717 4.453862 4.469060 4.484309 4.499610 4.514964 4.530370 4.545828
## [27,] 4.424068 4.440077 4.456144 4.472269 4.488452 4.504694 4.520995 4.537355
## [28,] 4.409467 4.426334 4.443265 4.460261 4.477322 4.494448 4.511640 4.528897
## [29,] 4.394915 4.412634 4.430424 4.448285 4.466219 4.484225 4.502304 4.520456
## [30,] 4.380411 4.398976 4.417619 4.436342 4.455144 4.474026 4.492987 4.512030
## [31,] 4.365954 4.385360 4.404852 4.424431 4.444096 4.463849 4.483690 4.503619
## [32,] 4.351546 4.371786 4.392122 4.412551 4.433076 4.453696 4.474412 4.495225
## [33,] 4.337184 4.358255 4.379428 4.400704 4.422083 4.443566 4.465153 4.486845
## [34,] 4.322871 4.344765 4.366771 4.388888 4.411117 4.433459 4.455914 4.478482
## [35,] 4.308604 4.331317 4.354151 4.377104 4.400178 4.423375 4.446693 4.470134
## [36,] 4.294385 4.317911 4.341567 4.365352 4.389267 4.413313 4.437491 4.461802
## [37,] 4.280212 4.304547 4.329019 4.353631 4.378383 4.403275 4.428309 4.453485
## [38,] 4.266087 4.291223 4.316508 4.341942 4.367525 4.393260 4.419146 4.445184
## [39,] 4.252007 4.277941 4.304033 4.330284 4.356695 4.383267 4.410001 4.436898
## [40,] 4.237975 4.264700 4.291594 4.318657 4.345891 4.373297 4.400875 4.428628
## [41,] 4.223988 4.251500 4.279191 4.307062 4.335114 4.363350 4.391769 4.420373
## [42,] 4.210048 4.238341 4.266823 4.295497 4.324364 4.353425 4.382681 4.412134
## [43,] 4.196154 4.225222 4.254492 4.283964 4.313641 4.343523 4.373612 4.403909
## [44,] 4.182306 4.212144 4.242196 4.272462 4.302944 4.333643 4.364562 4.395701
## [45,] 4.168503 4.199107 4.229936 4.260991 4.292273 4.323786 4.355530 4.387507
## [46,] 4.154746 4.186110 4.217711 4.249550 4.281630 4.313951 4.346517 4.379329
## [47,] 4.141034 4.173153 4.205521 4.238140 4.271012 4.304139 4.337523 4.371166
## [48,] 4.127368 4.160237 4.193367 4.226761 4.260421 4.294349 4.328547 4.363018
## [49,] 4.113747 4.147360 4.181248 4.215412 4.249856 4.284581 4.319590 4.354885
## [50,] 4.100170 4.134523 4.169163 4.204094 4.239317 4.274836 4.310652 4.346768
## [51,] 4.086639 4.121726 4.157114 4.192806 4.228805 4.265112 4.301732 4.338666
## [52,] 4.073152 4.108968 4.145100 4.181549 4.218318 4.255411 4.292830 4.330578
## [53,] 4.059710 4.096250 4.133120 4.170322 4.207858 4.245732 4.283947 4.322506
## [54,] 4.046312 4.083572 4.121175 4.159124 4.197423 4.236075 4.275082 4.314449
## [55,] 4.032958 4.070932 4.109264 4.147957 4.187015 4.226440 4.266236 4.306407
## [56,] 4.019648 4.058332 4.097388 4.136820 4.176632 4.216826 4.257408 4.298380
## [57,] 4.006382 4.045771 4.085546 4.125713 4.166275 4.207235 4.248598 4.290368
## [58,] 3.993160 4.033248 4.073739 4.114636 4.155943 4.197665 4.239807 4.282371
## [59,] 3.979982 4.020765 4.061965 4.103588 4.145637 4.188118 4.231033 4.274388
## [60,] 3.966847 4.008320 4.050226 4.092570 4.135357 4.178592 4.222278 4.266421
## [61,] 3.953755 3.995913 4.038520 4.081582 4.125102 4.169087 4.213541 4.258469
## [62,] 3.940707 3.983545 4.026849 4.070623 4.114873 4.159604 4.204822 4.250531
## [63,] 3.927702 3.971215 4.015211 4.059693 4.104669 4.150143 4.196121 4.242608
## [64,] 3.914739 3.958924 4.003606 4.048793 4.094490 4.140703 4.187438 4.234700
## [65,] 3.901820 3.946670 3.992036 4.037923 4.084337 4.131285 4.178773 4.226806
## [66,] 3.888943 3.934454 3.980498 4.027081 4.074209 4.121888 4.170126 4.218928
## [67,] 3.876109 3.922276 3.968994 4.016268 4.064106 4.112513 4.161496 4.211064
## [68,] 3.863316 3.910136 3.957523 4.005485 4.054028 4.103159 4.152885 4.203214
## [69,] 3.850567 3.898034 3.946086 3.994730 4.043975 4.093826 4.144292 4.195379
## [70,] 3.837859 3.885968 3.934681 3.984005 4.033946 4.084514 4.135716 4.187559
## [71,] 3.825193 3.873941 3.923310 3.973308 4.023943 4.075224 4.127158 4.179754
## [72,] 3.812569 3.861950 3.911971 3.962640 4.013965 4.065954 4.118618 4.171963
## [73,] 3.799986 3.849997 3.900665 3.952000 4.004011 4.056706 4.110095 4.164186
## [74,] 3.787446 3.838080 3.889392 3.941389 3.994082 4.047479 4.101590 4.156424
## [75,] 3.774946 3.826201 3.878151 3.930807 3.984177 4.038273 4.093103 4.148677
## [76,] 3.762488 3.814358 3.866943 3.920253 3.974298 4.029087 4.084633 4.140944
## [77,] 3.750071 3.802552 3.855767 3.909727 3.964442 4.019923 4.076180 4.133225
## [78,] 3.737695 3.790782 3.844623 3.899230 3.954611 4.010780 4.067746 4.125521
## [79,] 3.725359 3.779049 3.833512 3.888760 3.944805 4.001657 4.059328 4.117831
## [80,] 3.713065 3.767352 3.822433 3.878319 3.935022 3.992555 4.050928 4.110155
## [81,] 3.700811 3.755691 3.811386 3.867906 3.925264 3.983474 4.042546 4.102494
## [82,] 3.688597 3.744067 3.800370 3.857521 3.915531 3.974413 4.034181 4.094847
## [83,] 3.676424 3.732478 3.789387 3.847164 3.905821 3.965373 4.025833 4.087214
## [84,] 3.664291 3.720925 3.778435 3.836834 3.896136 3.956353 4.017502 4.079596
## [85,] 3.652198 3.709409 3.767515 3.826532 3.886474 3.947354 4.009189 4.071991
## [86,] 3.640145 3.697927 3.756627 3.816258 3.876836 3.938376 4.000893 4.064401
## [87,] 3.628131 3.686481 3.745770 3.806012 3.867223 3.929418 3.992613 4.056825
## [88,] 3.616158 3.675071 3.734944 3.795793 3.857633 3.920480 3.984352 4.049264
## [89,] 3.604224 3.663696 3.724150 3.785601 3.848067 3.911563 3.976107 4.041716
## [90,] 3.592329 3.652356 3.713387 3.775437 3.838524 3.902666 3.967879 4.034182
## [91,] 3.580473 3.641052 3.702655 3.765300 3.829006 3.893789 3.959668 4.026662
## [92,] 3.568657 3.629782 3.691954 3.755191 3.819511 3.884932 3.951475 4.019157
## [93,] 3.556879 3.618547 3.681284 3.745108 3.810039 3.876096 3.943298 4.011665
## [94,] 3.545141 3.607347 3.670644 3.735053 3.800591 3.867280 3.935138 4.004187
## [95,] 3.533441 3.596181 3.660036 3.725024 3.791167 3.858483 3.926995 3.996724
## [96,] 3.521780 3.585051 3.649458 3.715023 3.781765 3.849707 3.918869 3.989274
## [97,] 3.510157 3.573954 3.638911 3.705048 3.772387 3.840950 3.910760 3.981838
## [98,] 3.498573 3.562892 3.628394 3.695100 3.763033 3.832214 3.902667 3.974416
## [99,] 3.487027 3.551864 3.617908 3.685179 3.753701 3.823497 3.894592 3.967008
## [,17] [,18] [,19] [,20] [,21] [,22] [,23] [,24]
## [1,] 4.754620 4.746371 4.738137 4.729917 4.721711 4.713519 4.705342 4.697179
## [2,] 4.746734 4.739473 4.732224 4.724987 4.717760 4.710544 4.703339 4.696146
## [3,] 4.738860 4.732586 4.726320 4.720062 4.713812 4.707570 4.701337 4.695112
## [4,] 4.731000 4.725708 4.720422 4.715142 4.709867 4.704599 4.699336 4.694079
## [5,] 4.723153 4.718841 4.714532 4.710227 4.705926 4.701629 4.697336 4.693047
## [6,] 4.715319 4.711983 4.708649 4.705317 4.701988 4.698661 4.695336 4.692014
## [7,] 4.707498 4.705135 4.702773 4.700413 4.698053 4.695695 4.693338 4.690982
## [8,] 4.699690 4.698298 4.696905 4.695513 4.694122 4.692731 4.691340 4.689950
## [9,] 4.691895 4.691470 4.691044 4.690619 4.690194 4.689768 4.689343 4.688918
## [10,] 4.684113 4.684652 4.685191 4.685730 4.686269 4.686808 4.687347 4.687886
## [11,] 4.676344 4.677844 4.679344 4.680846 4.682347 4.683849 4.685352 4.686855
## [12,] 4.668587 4.671046 4.673506 4.675967 4.678429 4.680892 4.683357 4.685823
## [13,] 4.660844 4.664258 4.667674 4.671093 4.674514 4.677937 4.681364 4.684792
## [14,] 4.653113 4.657479 4.661849 4.666224 4.670602 4.674984 4.679371 4.683762
## [15,] 4.645395 4.650711 4.656032 4.661360 4.666694 4.672033 4.677379 4.682731
## [16,] 4.637690 4.643952 4.650222 4.656501 4.662788 4.669084 4.675388 4.681701
## [17,] 4.629998 4.637203 4.644420 4.651648 4.658886 4.666137 4.673398 4.680671
## [18,] 4.622319 4.630464 4.638624 4.646799 4.654988 4.663191 4.671409 4.679641
## [19,] 4.614652 4.623735 4.632836 4.641955 4.651092 4.660247 4.669420 4.678611
## [20,] 4.606998 4.617016 4.627055 4.637117 4.647200 4.657305 4.667433 4.677582
## [21,] 4.599357 4.610306 4.621282 4.632283 4.643311 4.654366 4.665446 4.676553
## [22,] 4.591728 4.603606 4.615515 4.627455 4.639426 4.651427 4.663460 4.675524
## [23,] 4.584112 4.596916 4.609756 4.622632 4.635543 4.648491 4.661475 4.674495
## [24,] 4.576509 4.590236 4.604004 4.617813 4.631664 4.645557 4.659491 4.673467
## [25,] 4.568918 4.583565 4.598259 4.613000 4.627788 4.642624 4.657507 4.672438
## [26,] 4.561340 4.576904 4.592521 4.608192 4.623916 4.639693 4.655525 4.671410
## [27,] 4.553774 4.570252 4.586790 4.603388 4.620046 4.636765 4.653543 4.670383
## [28,] 4.546221 4.563611 4.581067 4.598590 4.616180 4.633837 4.651562 4.669355
## [29,] 4.538680 4.556979 4.575351 4.593797 4.612317 4.630912 4.649582 4.668328
## [30,] 4.531152 4.550356 4.569641 4.589008 4.608457 4.627989 4.647603 4.667301
## [31,] 4.523637 4.543743 4.563939 4.584225 4.604601 4.625067 4.645625 4.666274
## [32,] 4.516134 4.537140 4.558244 4.579447 4.600748 4.622148 4.643647 4.665247
## [33,] 4.508643 4.530547 4.552557 4.574673 4.596898 4.619230 4.641671 4.664221
## [34,] 4.501165 4.523963 4.546876 4.569905 4.593051 4.616314 4.639695 4.663194
## [35,] 4.493699 4.517388 4.541202 4.565142 4.589207 4.613400 4.637720 4.662168
## [36,] 4.486246 4.510823 4.535536 4.560383 4.585367 4.610488 4.635746 4.661143
## [37,] 4.478805 4.504268 4.529876 4.555630 4.581530 4.607577 4.633773 4.660117
## [38,] 4.471376 4.497722 4.524224 4.550881 4.577696 4.604669 4.631800 4.659092
## [39,] 4.463960 4.491186 4.518578 4.546138 4.573865 4.601762 4.629829 4.658067
## [40,] 4.456555 4.484659 4.512940 4.541399 4.570038 4.598857 4.627858 4.657042
## [41,] 4.449164 4.478142 4.507309 4.536665 4.566213 4.595954 4.625888 4.656017
## [42,] 4.441784 4.471634 4.501684 4.531937 4.562392 4.593053 4.623919 4.654993
## [43,] 4.434417 4.465135 4.496067 4.527213 4.558574 4.590153 4.621951 4.653969
## [44,] 4.427062 4.458647 4.490457 4.522494 4.554760 4.587256 4.619983 4.652945
## [45,] 4.419719 4.452167 4.484854 4.517780 4.550948 4.584360 4.618017 4.651921
## [46,] 4.412388 4.445697 4.479257 4.513071 4.547140 4.581466 4.616051 4.650897
## [47,] 4.405070 4.439236 4.473668 4.508367 4.543335 4.578574 4.614086 4.649874
## [48,] 4.397763 4.432785 4.468086 4.503667 4.539533 4.575684 4.612122 4.648851
## [49,] 4.390469 4.426343 4.462510 4.498973 4.535734 4.572795 4.610159 4.647828
## [50,] 4.383187 4.419910 4.456942 4.494284 4.531938 4.569908 4.608197 4.646806
## [51,] 4.375916 4.413487 4.451380 4.489599 4.528146 4.567024 4.606235 4.645783
## [52,] 4.368658 4.407073 4.445826 4.484919 4.524357 4.564141 4.604274 4.644761
## [53,] 4.361412 4.400669 4.440278 4.480245 4.520571 4.561259 4.602315 4.643739
## [54,] 4.354178 4.394273 4.434738 4.475575 4.516788 4.558380 4.600355 4.642717
## [55,] 4.346956 4.387888 4.429204 4.470910 4.513008 4.555503 4.598397 4.641696
## [56,] 4.339746 4.381511 4.423677 4.466249 4.509231 4.552627 4.596440 4.640675
## [57,] 4.332548 4.375143 4.418157 4.461594 4.505458 4.549753 4.594483 4.639654
## [58,] 4.325362 4.368785 4.412644 4.456944 4.501688 4.546881 4.592528 4.638633
## [59,] 4.318188 4.362436 4.407138 4.452298 4.497920 4.544010 4.590573 4.637612
## [60,] 4.311026 4.356097 4.401639 4.447657 4.494156 4.541142 4.588619 4.636592
## [61,] 4.303875 4.349766 4.396146 4.443021 4.490396 4.538275 4.586666 4.635572
## [62,] 4.296737 4.343445 4.390661 4.438390 4.486638 4.535411 4.584713 4.634552
## [63,] 4.289610 4.337133 4.385182 4.433764 4.482883 4.532547 4.582762 4.633532
## [64,] 4.282495 4.330830 4.379710 4.429142 4.479132 4.529686 4.580811 4.632513
## [65,] 4.275392 4.324536 4.374245 4.424525 4.475384 4.526827 4.578861 4.631493
## [66,] 4.268301 4.318251 4.368787 4.419914 4.471639 4.523969 4.576912 4.630474
## [67,] 4.261221 4.311976 4.363335 4.415307 4.467897 4.521113 4.574964 4.629456
## [68,] 4.254153 4.305710 4.357891 4.410704 4.464158 4.518259 4.573016 4.628437
## [69,] 4.247097 4.299452 4.352453 4.406107 4.460422 4.515407 4.571070 4.627419
## [70,] 4.240053 4.293204 4.347022 4.401514 4.456690 4.512557 4.569124 4.626401
## [71,] 4.233020 4.286965 4.341598 4.396926 4.452960 4.509708 4.567179 4.625383
## [72,] 4.225999 4.280735 4.336180 4.392343 4.449234 4.506861 4.565235 4.624365
## [73,] 4.218990 4.274514 4.330769 4.387765 4.445511 4.504016 4.563292 4.623348
## [74,] 4.211992 4.268302 4.325365 4.383191 4.441790 4.501173 4.561349 4.622330
## [75,] 4.205006 4.262099 4.319968 4.378623 4.438074 4.498332 4.559408 4.621313
## [76,] 4.198031 4.255905 4.314578 4.374059 4.434360 4.495492 4.557467 4.620297
## [77,] 4.191068 4.249720 4.309194 4.369499 4.430649 4.492654 4.555527 4.619280
## [78,] 4.184117 4.243545 4.303817 4.364945 4.426941 4.489818 4.553588 4.618264
## [79,] 4.177177 4.237378 4.298446 4.360395 4.423237 4.486984 4.551650 4.617248
## [80,] 4.170248 4.231220 4.293083 4.355850 4.419535 4.484151 4.549712 4.616232
## [81,] 4.163331 4.225071 4.287726 4.351310 4.415837 4.481321 4.547776 4.615216
## [82,] 4.156426 4.218931 4.282375 4.346774 4.412141 4.478492 4.545840 4.614201
## [83,] 4.149532 4.212799 4.277032 4.342243 4.408449 4.475665 4.543905 4.613185
## [84,] 4.142649 4.206677 4.271695 4.337717 4.404760 4.472839 4.541971 4.612170
## [85,] 4.135778 4.200564 4.266365 4.333196 4.401074 4.470016 4.540037 4.611156
## [86,] 4.128918 4.194459 4.261041 4.328679 4.397391 4.467194 4.538105 4.610141
## [87,] 4.122070 4.188364 4.255724 4.324167 4.393711 4.464374 4.536173 4.609127
## [88,] 4.115233 4.182277 4.250414 4.319660 4.390035 4.461556 4.534242 4.608113
## [89,] 4.108407 4.176199 4.245110 4.315157 4.386361 4.458739 4.532312 4.607099
## [90,] 4.101593 4.170130 4.239813 4.310660 4.382690 4.455925 4.530383 4.606085
## [91,] 4.094790 4.164070 4.234522 4.306166 4.379023 4.453112 4.528455 4.605072
## [92,] 4.087998 4.158019 4.229238 4.301678 4.375358 4.450301 4.526527 4.604059
## [93,] 4.081218 4.151976 4.223961 4.297194 4.371697 4.447492 4.524600 4.603046
## [94,] 4.074448 4.145942 4.218690 4.292715 4.368039 4.444684 4.522674 4.602033
## [95,] 4.067690 4.139917 4.213426 4.288241 4.364383 4.441878 4.520749 4.601020
## [96,] 4.060943 4.133901 4.208169 4.283771 4.360731 4.439074 4.518825 4.600008
## [97,] 4.054208 4.127893 4.202918 4.279306 4.357082 4.436272 4.516901 4.598996
## [98,] 4.047483 4.121894 4.197673 4.274845 4.353436 4.433472 4.514979 4.597984
## [99,] 4.040770 4.115904 4.192435 4.270389 4.349793 4.430673 4.513057 4.596972
## [,25] [,26] [,27] [,28] [,29] [,30] [,31] [,32]
## [1,] 4.689030 4.680895 4.672775 4.664668 4.656575 4.648497 4.640432 4.632382
## [2,] 4.688963 4.681791 4.674630 4.667481 4.660342 4.653214 4.646097 4.638991
## [3,] 4.688896 4.682687 4.676487 4.670295 4.664111 4.657936 4.651768 4.645609
## [4,] 4.688828 4.683583 4.678344 4.673111 4.667884 4.662662 4.657446 4.652237
## [5,] 4.688761 4.684480 4.680202 4.675929 4.671659 4.667393 4.663132 4.658874
## [6,] 4.688694 4.685376 4.682061 4.678748 4.675438 4.672130 4.668824 4.665520
## [7,] 4.688627 4.686273 4.683921 4.681570 4.679219 4.676871 4.674523 4.672176
## [8,] 4.688560 4.687170 4.685781 4.684392 4.683004 4.681616 4.680229 4.678842
## [9,] 4.688492 4.688067 4.687642 4.687217 4.686792 4.686367 4.685942 4.685517
## [10,] 4.688425 4.688965 4.689504 4.690043 4.690583 4.691122 4.691662 4.692202
## [11,] 4.688358 4.689862 4.691366 4.692871 4.694377 4.695883 4.697389 4.698896
## [12,] 4.688291 4.690760 4.693230 4.695701 4.698174 4.700648 4.703123 4.705600
## [13,] 4.688224 4.691657 4.695094 4.698532 4.701974 4.705418 4.708864 4.712313
## [14,] 4.688156 4.692555 4.696958 4.701366 4.705777 4.710192 4.714612 4.719036
## [15,] 4.688089 4.693454 4.698824 4.704200 4.709583 4.714972 4.720367 4.725768
## [16,] 4.688022 4.694352 4.700690 4.707037 4.713392 4.719756 4.726129 4.732510
## [17,] 4.687955 4.695250 4.702557 4.709875 4.717205 4.724546 4.731898 4.739262
## [18,] 4.687888 4.696149 4.704425 4.712715 4.721020 4.729340 4.737674 4.746023
## [19,] 4.687821 4.697048 4.706293 4.715557 4.724839 4.734139 4.743457 4.752794
## [20,] 4.687753 4.697947 4.708162 4.718400 4.728660 4.738943 4.749247 4.759575
## [21,] 4.687686 4.698846 4.710032 4.721245 4.732485 4.743751 4.755045 4.766365
## [22,] 4.687619 4.699745 4.711903 4.724092 4.736313 4.748565 4.760849 4.773165
## [23,] 4.687552 4.700645 4.713774 4.726941 4.740144 4.753384 4.766661 4.779975
## [24,] 4.687485 4.701544 4.715647 4.729791 4.743978 4.758207 4.772479 4.786794
## [25,] 4.687417 4.702444 4.717519 4.732643 4.747815 4.763035 4.778305 4.793623
## [26,] 4.687350 4.703344 4.719393 4.735497 4.751655 4.767869 4.784137 4.800462
## [27,] 4.687283 4.704245 4.721267 4.738352 4.755498 4.772707 4.789977 4.807311
## [28,] 4.687216 4.705145 4.723143 4.741209 4.759345 4.777550 4.795824 4.814169
## [29,] 4.687149 4.706045 4.725018 4.744068 4.763194 4.782398 4.801678 4.821037
## [30,] 4.687082 4.706946 4.726895 4.746929 4.767047 4.787251 4.807540 4.827915
## [31,] 4.687014 4.707847 4.728772 4.749791 4.770903 4.792108 4.813408 4.834803
## [32,] 4.686947 4.708748 4.730651 4.752655 4.774762 4.796971 4.819284 4.841700
## [33,] 4.686880 4.709649 4.732529 4.755521 4.778624 4.801839 4.825167 4.848608
## [34,] 4.686813 4.710551 4.734409 4.758388 4.782489 4.806711 4.831057 4.855525
## [35,] 4.686746 4.711452 4.736289 4.761257 4.786357 4.811589 4.836954 4.862452
## [36,] 4.686678 4.712354 4.738171 4.764128 4.790228 4.816471 4.842858 4.869389
## [37,] 4.686611 4.713256 4.740052 4.767001 4.794103 4.821359 4.848770 4.876336
## [38,] 4.686544 4.714158 4.741935 4.769875 4.797980 4.826251 4.854688 4.883293
## [39,] 4.686477 4.715060 4.743818 4.772752 4.801861 4.831148 4.860614 4.890260
## [40,] 4.686410 4.715963 4.745702 4.775629 4.805745 4.836051 4.866548 4.897237
## [41,] 4.686343 4.716866 4.747587 4.778509 4.809632 4.840958 4.872488 4.904223
## [42,] 4.686275 4.717768 4.749473 4.781390 4.813522 4.845870 4.878436 4.911220
## [43,] 4.686208 4.718671 4.751359 4.784273 4.817416 4.850788 4.884391 4.918227
## [44,] 4.686141 4.719574 4.753246 4.787158 4.821312 4.855710 4.890353 4.925243
## [45,] 4.686074 4.720478 4.755134 4.790045 4.825212 4.860637 4.896322 4.932270
## [46,] 4.686007 4.721381 4.757023 4.792933 4.829115 4.865569 4.902299 4.939306
## [47,] 4.685940 4.722285 4.758912 4.795823 4.833021 4.870507 4.908283 4.946353
## [48,] 4.685872 4.723189 4.760802 4.798715 4.836930 4.875449 4.914275 4.953410
## [49,] 4.685805 4.724093 4.762693 4.801608 4.840842 4.880396 4.920274 4.960477
## [50,] 4.685738 4.724997 4.764584 4.804504 4.844757 4.885348 4.926280 4.967554
## [51,] 4.685671 4.725901 4.766477 4.807401 4.848676 4.890306 4.932293 4.974641
## [52,] 4.685604 4.726806 4.768370 4.810300 4.852598 4.895268 4.938314 4.981738
## [53,] 4.685537 4.727710 4.770264 4.813200 4.856523 4.900236 4.944342 4.988845
## [54,] 4.685470 4.728615 4.772158 4.816102 4.860451 4.905208 4.950377 4.995962
## [55,] 4.685402 4.729520 4.774054 4.819006 4.864382 4.910185 4.956420 5.003090
## [56,] 4.685335 4.730426 4.775950 4.821912 4.868317 4.915168 4.962470 5.010227
## [57,] 4.685268 4.731331 4.777847 4.824820 4.872254 4.920156 4.968528 5.017375
## [58,] 4.685201 4.732236 4.779744 4.827729 4.876195 4.925148 4.974593 5.024533
## [59,] 4.685134 4.733142 4.781643 4.830640 4.880139 4.930146 4.980665 5.031702
## [60,] 4.685067 4.734048 4.783542 4.833553 4.884087 4.935149 4.986745 5.038880
## [61,] 4.684999 4.734954 4.785442 4.836467 4.888037 4.940157 4.992832 5.046069
## [62,] 4.684932 4.735860 4.787342 4.839383 4.891991 4.945170 4.998927 5.053268
## [63,] 4.684865 4.736767 4.789244 4.842302 4.895947 4.950188 5.005029 5.060477
## [64,] 4.684798 4.737673 4.791146 4.845221 4.899907 4.955211 5.011138 5.067697
## [65,] 4.684731 4.738580 4.793049 4.848143 4.903871 4.960239 5.017255 5.074927
## [66,] 4.684664 4.739487 4.794952 4.851066 4.907837 4.965272 5.023380 5.082167
## [67,] 4.684597 4.740394 4.796857 4.853991 4.911807 4.970311 5.029511 5.089417
## [68,] 4.684529 4.741302 4.798762 4.856918 4.915780 4.975354 5.035651 5.096678
## [69,] 4.684462 4.742209 4.800668 4.859847 4.919756 4.980403 5.041798 5.103949
## [70,] 4.684395 4.743117 4.802574 4.862777 4.923735 4.985457 5.047952 5.111231
## [71,] 4.684328 4.744024 4.804482 4.865709 4.927717 4.990516 5.054114 5.118523
## [72,] 4.684261 4.744932 4.806390 4.868643 4.931703 4.995580 5.060283 5.125825
## [73,] 4.684194 4.745841 4.808299 4.871579 4.935692 5.000649 5.066460 5.133138
## [74,] 4.684127 4.746749 4.810209 4.874516 4.939684 5.005723 5.072645 5.140461
## [75,] 4.684059 4.747657 4.812119 4.877456 4.943680 5.010803 5.078837 5.147795
## [76,] 4.683992 4.748566 4.814030 4.880397 4.947678 5.015887 5.085037 5.155139
## [77,] 4.683925 4.749475 4.815942 4.883339 4.951680 5.020977 5.091244 5.162494
## [78,] 4.683858 4.750384 4.817855 4.886284 4.955685 5.026072 5.097458 5.169859
## [79,] 4.683791 4.751293 4.819768 4.889230 4.959693 5.031172 5.103681 5.177234
## [80,] 4.683724 4.752203 4.821683 4.892178 4.963705 5.036277 5.109911 5.184621
## [81,] 4.683657 4.753112 4.823598 4.895128 4.967720 5.041388 5.116148 5.192017
## [82,] 4.683590 4.754022 4.825513 4.898080 4.971738 5.046503 5.122393 5.199424
## [83,] 4.683522 4.754932 4.827430 4.901033 4.975759 5.051624 5.128646 5.206842
## [84,] 4.683455 4.755842 4.829347 4.903989 4.979784 5.056750 5.134907 5.214271
## [85,] 4.683388 4.756752 4.831265 4.906946 4.983812 5.061882 5.141175 5.221710
## [86,] 4.683321 4.757663 4.833184 4.909905 4.987843 5.067018 5.147450 5.229159
## [87,] 4.683254 4.758573 4.835104 4.912865 4.991877 5.072160 5.153734 5.236619
## [88,] 4.683187 4.759484 4.837024 4.915827 4.995915 5.077307 5.160025 5.244090
## [89,] 4.683120 4.760395 4.838945 4.918792 4.999956 5.082459 5.166323 5.251572
## [90,] 4.683053 4.761306 4.840867 4.921758 5.004000 5.087616 5.172630 5.259064
## [91,] 4.682985 4.762217 4.842790 4.924725 5.008047 5.092779 5.178944 5.266567
## [92,] 4.682918 4.763129 4.844713 4.927695 5.012098 5.097946 5.185266 5.274080
## [93,] 4.682851 4.764040 4.846637 4.930666 5.016152 5.103120 5.191595 5.281605
## [94,] 4.682784 4.764952 4.848562 4.933639 5.020209 5.108298 5.197932 5.289140
## [95,] 4.682717 4.765864 4.850488 4.936614 5.024270 5.113481 5.204277 5.296686
## [96,] 4.682650 4.766776 4.852414 4.939591 5.028333 5.118670 5.210630 5.304242
## [97,] 4.682583 4.767689 4.854341 4.942569 5.032400 5.123864 5.216991 5.311809
## [98,] 4.682516 4.768601 4.856269 4.945549 5.036471 5.129064 5.223359 5.319388
## [99,] 4.682449 4.769514 4.858198 4.948532 5.040544 5.134268 5.229735 5.326976
## [,33] [,34] [,35] [,36] [,37] [,38] [,39] [,40]
## [1,] 4.624345 4.616323 4.608314 4.600319 4.592338 4.584371 4.576418 4.568478
## [2,] 4.631895 4.624811 4.617737 4.610674 4.603623 4.596581 4.589551 4.582531
## [3,] 4.639458 4.633315 4.627180 4.621053 4.614935 4.608824 4.602722 4.596627
## [4,] 4.647032 4.641834 4.636642 4.631455 4.626274 4.621099 4.615930 4.610767
## [5,] 4.654620 4.650369 4.646123 4.641881 4.637642 4.633407 4.629177 4.624950
## [6,] 4.662219 4.658920 4.655624 4.652330 4.649038 4.645748 4.642461 4.639176
## [7,] 4.669831 4.667487 4.665144 4.662802 4.660461 4.658122 4.655784 4.653446
## [8,] 4.677455 4.676069 4.674683 4.673298 4.671913 4.670529 4.669144 4.667761
## [9,] 4.685092 4.684667 4.684242 4.683818 4.683393 4.682968 4.682544 4.682119
## [10,] 4.692741 4.693281 4.693821 4.694361 4.694901 4.695441 4.695981 4.696521
## [11,] 4.700403 4.701911 4.703419 4.704928 4.706437 4.707947 4.709457 4.710968
## [12,] 4.708077 4.710557 4.713037 4.715519 4.718002 4.720486 4.722972 4.725459
## [13,] 4.715764 4.719218 4.722675 4.726134 4.729595 4.733059 4.736526 4.739995
## [14,] 4.723464 4.727896 4.732332 4.736772 4.741217 4.745665 4.750118 4.754575
## [15,] 4.731175 4.736589 4.742009 4.747435 4.752867 4.758305 4.763750 4.769201
## [16,] 4.738900 4.745298 4.751705 4.758121 4.764546 4.770979 4.777420 4.783871
## [17,] 4.746637 4.754024 4.761422 4.768832 4.776253 4.783686 4.791130 4.798586
## [18,] 4.754387 4.762765 4.771158 4.779566 4.787989 4.796427 4.804879 4.813347
## [19,] 4.762149 4.771523 4.780915 4.790325 4.799754 4.809202 4.818668 4.828153
## [20,] 4.769924 4.780296 4.790691 4.801108 4.811548 4.822011 4.832496 4.843005
## [21,] 4.777712 4.789086 4.800487 4.811916 4.823371 4.834854 4.846364 4.857902
## [22,] 4.785513 4.797892 4.810304 4.822747 4.835223 4.847731 4.860272 4.872845
## [23,] 4.793326 4.806714 4.820140 4.833603 4.847104 4.860643 4.874220 4.887834
## [24,] 4.801152 4.815553 4.829997 4.844484 4.859015 4.873589 4.888207 4.902869
## [25,] 4.808990 4.824407 4.839873 4.855389 4.870954 4.886570 4.902235 4.917951
## [26,] 4.816842 4.833278 4.849770 4.866318 4.882923 4.899585 4.916303 4.933078
## [27,] 4.824706 4.842165 4.859687 4.877273 4.894922 4.912635 4.930412 4.948253
## [28,] 4.832584 4.851069 4.869625 4.888251 4.906949 4.925719 4.944560 4.963474
## [29,] 4.840474 4.859989 4.879582 4.899255 4.919007 4.938838 4.958750 4.978742
## [30,] 4.848377 4.868925 4.889560 4.910283 4.931094 4.951993 4.972980 4.994057
## [31,] 4.856292 4.877878 4.899559 4.921336 4.943211 4.965182 4.987251 5.009418
## [32,] 4.864221 4.886847 4.909578 4.932414 4.955357 4.978407 5.001563 5.024828
## [33,] 4.872163 4.895833 4.919617 4.943517 4.967533 4.991666 5.015916 5.040284
## [34,] 4.880118 4.904835 4.929677 4.954645 4.979740 5.004961 5.030311 5.055788
## [35,] 4.888085 4.913853 4.939757 4.965798 4.991976 5.018292 5.044746 5.071340
## [36,] 4.896066 4.922889 4.949859 4.976976 5.004242 5.031658 5.059223 5.086940
## [37,] 4.904060 4.931941 4.959980 4.988179 5.016539 5.045059 5.073742 5.102588
## [38,] 4.912066 4.941009 4.970123 4.999408 5.028865 5.058496 5.088302 5.118283
## [39,] 4.920086 4.950095 4.980286 5.010661 5.041222 5.071969 5.102904 5.134027
## [40,] 4.928119 4.959197 4.990470 5.021941 5.053610 5.085478 5.117548 5.149820
## [41,] 4.936165 4.968315 5.000675 5.033245 5.066027 5.099023 5.132234 5.165661
## [42,] 4.944224 4.977451 5.010900 5.044575 5.078476 5.112604 5.146962 5.181551
## [43,] 4.952297 4.986603 5.021147 5.055930 5.090954 5.126221 5.161732 5.197489
## [44,] 4.960382 4.995772 5.031415 5.067311 5.103464 5.139875 5.176545 5.213477
## [45,] 4.968481 5.004958 5.041703 5.078718 5.116004 5.153564 5.191400 5.229514
## [46,] 4.976593 5.014161 5.052013 5.090150 5.128575 5.167291 5.206298 5.245600
## [47,] 4.984718 5.023381 5.062343 5.101608 5.141177 5.181053 5.221239 5.261736
## [48,] 4.992857 5.032618 5.072695 5.113092 5.153810 5.194853 5.236222 5.277921
## [49,] 5.001008 5.041871 5.083068 5.124601 5.166474 5.208689 5.251249 5.294156
## [50,] 5.009173 5.051142 5.093462 5.136137 5.179169 5.222562 5.266318 5.310441
## [51,] 5.017352 5.060430 5.103878 5.147698 5.191895 5.236472 5.281431 5.326776
## [52,] 5.025544 5.069735 5.114314 5.159286 5.204653 5.250419 5.296587 5.343162
## [53,] 5.033749 5.079057 5.124772 5.170900 5.217442 5.264403 5.311787 5.359598
## [54,] 5.041967 5.088396 5.135252 5.182539 5.230262 5.278425 5.327031 5.376084
## [55,] 5.050199 5.097752 5.145753 5.194205 5.243114 5.292483 5.342318 5.392621
## [56,] 5.058444 5.107125 5.156275 5.205897 5.255997 5.306580 5.357649 5.409209
## [57,] 5.066703 5.116516 5.166819 5.217616 5.268913 5.320713 5.373024 5.425848
## [58,] 5.074976 5.125924 5.177384 5.229361 5.281859 5.334885 5.388443 5.442538
## [59,] 5.083261 5.135349 5.187971 5.241132 5.294838 5.349094 5.403906 5.459280
## [60,] 5.091561 5.144792 5.198580 5.252930 5.307848 5.363341 5.419414 5.476073
## [61,] 5.099874 5.154252 5.209210 5.264754 5.320891 5.377626 5.434966 5.492917
## [62,] 5.108200 5.163729 5.219862 5.276605 5.333965 5.391949 5.450563 5.509814
## [63,] 5.116540 5.173224 5.230536 5.288483 5.347072 5.406310 5.466204 5.526762
## [64,] 5.124894 5.182736 5.241232 5.300388 5.360211 5.420709 5.481891 5.543763
## [65,] 5.133261 5.192266 5.251949 5.312319 5.373382 5.435147 5.497622 5.560816
## [66,] 5.141642 5.201813 5.262689 5.324277 5.386586 5.449623 5.513399 5.577921
## [67,] 5.150037 5.211378 5.273450 5.336262 5.399821 5.464138 5.529221 5.595079
## [68,] 5.158445 5.220961 5.284234 5.348274 5.413090 5.478692 5.545088 5.612289
## [69,] 5.166867 5.230561 5.295039 5.360313 5.426391 5.493284 5.561001 5.629553
## [70,] 5.175303 5.240178 5.305867 5.372379 5.439725 5.507915 5.576960 5.646870
## [71,] 5.183753 5.249814 5.316717 5.384472 5.453091 5.522585 5.592964 5.664240
## [72,] 5.192216 5.259467 5.327589 5.396593 5.466491 5.537294 5.609014 5.681663
## [73,] 5.200693 5.269138 5.338483 5.408741 5.479923 5.552042 5.625110 5.699140
## [74,] 5.209184 5.278826 5.349399 5.420916 5.493388 5.566830 5.641253 5.716671
## [75,] 5.217689 5.288533 5.360338 5.433118 5.506887 5.581657 5.657442 5.734256
## [76,] 5.226208 5.298257 5.371299 5.445348 5.520418 5.596523 5.673677 5.751895
## [77,] 5.234741 5.307999 5.382283 5.457606 5.533983 5.611429 5.689959 5.769588
## [78,] 5.243288 5.317759 5.393289 5.469891 5.547581 5.626375 5.706287 5.787335
## [79,] 5.251848 5.327537 5.404317 5.482204 5.561213 5.641360 5.722663 5.805137
## [80,] 5.260423 5.337333 5.415368 5.494544 5.574878 5.656386 5.739085 5.822994
## [81,] 5.269011 5.347147 5.426442 5.506912 5.588576 5.671451 5.755555 5.840906
## [82,] 5.277614 5.356979 5.437538 5.519309 5.602309 5.686557 5.772072 5.858873
## [83,] 5.286231 5.366830 5.448657 5.531733 5.616075 5.701702 5.788636 5.876895
## [84,] 5.294861 5.376698 5.459799 5.544185 5.629874 5.716889 5.805248 5.894973
## [85,] 5.303506 5.386584 5.470963 5.556665 5.643708 5.732115 5.821907 5.913106
## [86,] 5.312165 5.396489 5.482151 5.569173 5.657576 5.747382 5.838614 5.931295
## [87,] 5.320838 5.406412 5.493361 5.581709 5.671478 5.762690 5.855370 5.949540
## [88,] 5.329525 5.416353 5.504594 5.594273 5.685414 5.778039 5.872173 5.967841
## [89,] 5.338227 5.426312 5.515850 5.606866 5.699384 5.793428 5.889024 5.986198
## [90,] 5.346943 5.436289 5.527129 5.619487 5.713388 5.808859 5.905924 6.004612
## [91,] 5.355672 5.446285 5.538432 5.632137 5.727427 5.824330 5.922873 6.023082
## [92,] 5.364416 5.456300 5.549757 5.644815 5.741501 5.839843 5.939870 6.041610
## [93,] 5.373175 5.466333 5.561105 5.657521 5.755609 5.855397 5.956915 6.060194
## [94,] 5.381948 5.476384 5.572477 5.670257 5.769752 5.870993 5.974010 6.078835
## [95,] 5.390735 5.486453 5.583872 5.683020 5.783929 5.886630 5.991154 6.097534
## [96,] 5.399536 5.496542 5.595290 5.695813 5.798141 5.902308 6.008347 6.116290
## [97,] 5.408352 5.506648 5.606732 5.708634 5.812389 5.918029 6.025589 6.135104
## [98,] 5.417182 5.516774 5.618197 5.721484 5.826671 5.933791 6.042881 6.153976
## [99,] 5.426026 5.526918 5.629685 5.734363 5.840988 5.949595 6.060222 6.172906
## [,41] [,42] [,43] [,44] [,45] [,46] [,47] [,48]
## [1,] 4.560553 4.552641 4.544743 4.536858 4.528987 4.521130 4.513287 4.505457
## [2,] 4.575522 4.568524 4.561537 4.554560 4.547594 4.540638 4.533693 4.526759
## [3,] 4.590541 4.584463 4.578393 4.572331 4.566276 4.560230 4.554192 4.548162
## [4,] 4.605609 4.600457 4.595311 4.590171 4.585036 4.579907 4.574784 4.569667
## [5,] 4.620727 4.616507 4.612292 4.608080 4.603873 4.599669 4.595469 4.591273
## [6,] 4.635894 4.632613 4.629336 4.626060 4.622787 4.619516 4.616247 4.612981
## [7,] 4.651111 4.648776 4.646442 4.644110 4.641778 4.639448 4.637119 4.634792
## [8,] 4.666377 4.664994 4.663612 4.662230 4.660848 4.659467 4.658086 4.656706
## [9,] 4.681694 4.681270 4.680845 4.680421 4.679996 4.679572 4.679148 4.678723
## [10,] 4.697062 4.697602 4.698142 4.698683 4.699223 4.699764 4.700304 4.700845
## [11,] 4.712479 4.713991 4.715503 4.717016 4.718529 4.720042 4.721557 4.723071
## [12,] 4.727947 4.730437 4.732928 4.735420 4.737914 4.740409 4.742905 4.745403
## [13,] 4.743467 4.746941 4.750418 4.753897 4.757379 4.760863 4.764350 4.767840
## [14,] 4.759037 4.763502 4.767972 4.772445 4.776923 4.781406 4.785892 4.790383
## [15,] 4.774658 4.780121 4.785590 4.791066 4.796548 4.802037 4.807531 4.813032
## [16,] 4.790330 4.796798 4.803274 4.809760 4.816254 4.822757 4.829268 4.835789
## [17,] 4.806054 4.813533 4.821024 4.828526 4.836041 4.843566 4.851104 4.858653
## [18,] 4.821829 4.830327 4.838839 4.847366 4.855908 4.864466 4.873038 4.881626
## [19,] 4.837656 4.847179 4.856720 4.866279 4.875858 4.885455 4.895071 4.904707
## [20,] 4.853536 4.864090 4.874666 4.885266 4.895889 4.906535 4.917204 4.927897
## [21,] 4.869467 4.881059 4.892680 4.904327 4.916003 4.927706 4.939438 4.951197
## [22,] 4.885450 4.898089 4.910759 4.923463 4.936199 4.948969 4.961771 4.974607
## [23,] 4.901486 4.915177 4.928906 4.942673 4.956479 4.970323 4.984206 4.998127
## [24,] 4.917575 4.932325 4.947119 4.961958 4.976841 4.991769 5.006742 5.021759
## [25,] 4.933717 4.949533 4.965400 4.981318 4.997288 5.013308 5.029380 5.045503
## [26,] 4.949911 4.966801 4.983749 5.000754 5.017818 5.034940 5.052120 5.069359
## [27,] 4.966159 4.984129 5.002165 5.020266 5.038433 5.056665 5.074963 5.093327
## [28,] 4.982460 5.001518 5.020649 5.039854 5.059132 5.078484 5.097909 5.117409
## [29,] 4.998814 5.018967 5.039202 5.059518 5.079916 5.100397 5.120959 5.141605
## [30,] 5.015222 5.036478 5.057823 5.079259 5.100786 5.122404 5.144114 5.165915
## [31,] 5.031684 5.054049 5.076513 5.099077 5.121742 5.144507 5.167373 5.190341
## [32,] 5.048200 5.071682 5.095272 5.118973 5.142783 5.166704 5.190737 5.214881
## [33,] 5.064771 5.089376 5.114101 5.138946 5.163911 5.188998 5.214207 5.239538
## [34,] 5.081395 5.107132 5.132999 5.158996 5.185126 5.211388 5.237783 5.264311
## [35,] 5.098074 5.124950 5.151966 5.179126 5.206428 5.233874 5.261465 5.289202
## [36,] 5.114808 5.142830 5.171004 5.199333 5.227818 5.256458 5.285255 5.314210
## [37,] 5.131597 5.160772 5.190112 5.219620 5.249295 5.279139 5.309152 5.339336
## [38,] 5.148441 5.178777 5.209291 5.239985 5.270861 5.301917 5.333157 5.364581
## [39,] 5.165341 5.196845 5.228541 5.260431 5.292515 5.324795 5.357271 5.389946
## [40,] 5.182295 5.214976 5.247862 5.280956 5.314258 5.347770 5.381494 5.415430
## [41,] 5.199306 5.233170 5.267254 5.301561 5.336090 5.370845 5.405826 5.441035
## [42,] 5.216372 5.251427 5.286718 5.322246 5.358013 5.394020 5.430269 5.466761
## [43,] 5.233494 5.269748 5.306254 5.343012 5.380025 5.417294 5.454822 5.492609
## [44,] 5.250673 5.288134 5.325862 5.363859 5.402128 5.440669 5.479486 5.518579
## [45,] 5.267907 5.306583 5.345542 5.384788 5.424321 5.464145 5.504261 5.544672
## [46,] 5.285199 5.325097 5.365295 5.405798 5.446606 5.487722 5.529148 5.570888
## [47,] 5.302547 5.343675 5.385122 5.426890 5.468982 5.511401 5.554148 5.597228
## [48,] 5.319952 5.362318 5.405021 5.448064 5.491450 5.535182 5.579261 5.623692
## [49,] 5.337414 5.381026 5.424994 5.469321 5.514011 5.559065 5.604488 5.650282
## [50,] 5.354934 5.399799 5.445041 5.490661 5.536664 5.583052 5.629828 5.676997
## [51,] 5.372511 5.418638 5.465162 5.512084 5.559410 5.607142 5.655284 5.703839
## [52,] 5.390146 5.437543 5.485357 5.533591 5.582250 5.631336 5.680854 5.730807
## [53,] 5.407839 5.456514 5.505627 5.555182 5.605183 5.655634 5.706540 5.757903
## [54,] 5.425589 5.475550 5.525971 5.576857 5.628211 5.680038 5.732342 5.785128
## [55,] 5.443398 5.494653 5.546391 5.598616 5.651333 5.704546 5.758261 5.812481
## [56,] 5.461266 5.513823 5.566887 5.620461 5.674550 5.729161 5.784296 5.839963
## [57,] 5.479192 5.533060 5.587458 5.642390 5.697863 5.753881 5.810450 5.867575
## [58,] 5.497177 5.552364 5.608105 5.664406 5.721272 5.778708 5.836722 5.895318
## [59,] 5.515221 5.571735 5.628828 5.686507 5.744776 5.803643 5.863113 5.923192
## [60,] 5.533324 5.591174 5.649628 5.708694 5.768377 5.828685 5.889623 5.951197
## [61,] 5.551487 5.610680 5.670505 5.730968 5.792076 5.853835 5.916252 5.979336
## [62,] 5.569709 5.630255 5.691459 5.753329 5.815871 5.879093 5.943003 6.007607
## [63,] 5.587991 5.649898 5.712491 5.775777 5.839764 5.904461 5.969874 6.036012
## [64,] 5.606333 5.669609 5.733600 5.798313 5.863756 5.929938 5.996867 6.064551
## [65,] 5.624735 5.689389 5.754787 5.820936 5.887846 5.955525 6.023981 6.093225
## [66,] 5.643198 5.709239 5.776052 5.843648 5.912035 5.981222 6.051219 6.122034
## [67,] 5.661721 5.729157 5.797396 5.866449 5.936323 6.007030 6.078579 6.150980
## [68,] 5.680305 5.749145 5.818819 5.889338 5.960711 6.032950 6.106063 6.180063
## [69,] 5.698950 5.769203 5.840321 5.912317 5.985200 6.058981 6.133672 6.209283
## [70,] 5.717656 5.789330 5.861903 5.935385 6.009789 6.085125 6.161405 6.238642
## [71,] 5.736424 5.809528 5.883564 5.958544 6.034479 6.111381 6.189264 6.268139
## [72,] 5.755253 5.829797 5.905306 5.981792 6.059270 6.137751 6.217248 6.297776
## [73,] 5.774145 5.850136 5.927127 6.005132 6.084163 6.164234 6.245360 6.327552
## [74,] 5.793098 5.870546 5.949030 6.028562 6.109159 6.190832 6.273598 6.357470
## [75,] 5.812113 5.891027 5.971013 6.052084 6.134257 6.217545 6.301964 6.387529
## [76,] 5.831191 5.911580 5.993077 6.075698 6.159458 6.244373 6.330458 6.417730
## [77,] 5.850331 5.932204 6.015223 6.099404 6.184763 6.271316 6.359081 6.448074
## [78,] 5.869534 5.952901 6.037451 6.123202 6.210172 6.298376 6.387834 6.478562
## [79,] 5.888800 5.973669 6.059761 6.147094 6.235685 6.325553 6.416716 6.509193
## [80,] 5.908130 5.994510 6.082153 6.171078 6.261303 6.352847 6.445729 6.539970
## [81,] 5.927523 6.015424 6.104629 6.195156 6.287026 6.380259 6.474874 6.570892
## [82,] 5.946979 6.036411 6.127187 6.219328 6.312855 6.407788 6.504150 6.601960
## [83,] 5.966500 6.057470 6.149828 6.243594 6.338790 6.435437 6.533558 6.633175
## [84,] 5.986084 6.078604 6.172554 6.267955 6.364832 6.463205 6.563099 6.664537
## [85,] 6.005733 6.099811 6.195363 6.292411 6.390980 6.491093 6.592774 6.696048
## [86,] 6.025446 6.121092 6.218256 6.316963 6.417236 6.519101 6.622583 6.727708
## [87,] 6.045224 6.142447 6.241234 6.341610 6.443600 6.547230 6.652527 6.759518
## [88,] 6.065067 6.163877 6.264297 6.366353 6.470072 6.575481 6.682607 6.791478
## [89,] 6.084975 6.185382 6.287446 6.391193 6.496653 6.603853 6.712822 6.823589
## [90,] 6.104948 6.206962 6.310679 6.416130 6.523343 6.632348 6.743174 6.855852
## [91,] 6.124987 6.228616 6.333999 6.441164 6.550143 6.660966 6.773663 6.888267
## [92,] 6.145092 6.250347 6.357405 6.466296 6.577053 6.689707 6.804290 6.920836
## [93,] 6.165263 6.272153 6.380897 6.491526 6.604073 6.718572 6.835056 6.953559
## [94,] 6.185500 6.294036 6.404476 6.516855 6.631205 6.747562 6.865960 6.986436
## [95,] 6.205803 6.315994 6.428142 6.542282 6.658448 6.776676 6.897004 7.019469
## [96,] 6.226173 6.338030 6.451896 6.567808 6.685803 6.805917 6.928189 7.052658
## [97,] 6.246610 6.360142 6.475738 6.593434 6.713270 6.835284 6.959515 7.086004
## [98,] 6.267114 6.382331 6.499667 6.619160 6.740850 6.864777 6.990982 7.119508
## [99,] 6.287685 6.404598 6.523685 6.644986 6.768543 6.894397 7.022592 7.153170
## [,49] [,50] [,51] [,52] [,53] [,54] [,55] [,56]
## [1,] 4.497640 4.489837 4.482048 4.474272 4.466510 4.458761 4.451026 4.443304
## [2,] 4.519835 4.512922 4.506020 4.499128 4.492247 4.485376 4.478515 4.471666
## [3,] 4.542140 4.536126 4.530120 4.524122 4.518131 4.512149 4.506175 4.500208
## [4,] 4.564555 4.559449 4.554349 4.549254 4.544165 4.539082 4.534005 4.528933
## [5,] 4.587080 4.582892 4.578707 4.574526 4.570349 4.566176 4.562006 4.557841
## [6,] 4.609717 4.606455 4.603196 4.599939 4.596684 4.593431 4.590181 4.586933
## [7,] 4.632465 4.630140 4.627815 4.625492 4.623170 4.620850 4.618530 4.616212
## [8,] 4.655326 4.653946 4.652567 4.651188 4.649810 4.648432 4.647054 4.645677
## [9,] 4.678299 4.677875 4.677450 4.677026 4.676602 4.676178 4.675754 4.675330
## [10,] 4.701386 4.701926 4.702467 4.703008 4.703549 4.704090 4.704631 4.705173
## [11,] 4.724586 4.726102 4.727618 4.729134 4.730651 4.732169 4.733687 4.735205
## [12,] 4.747901 4.750402 4.752903 4.755406 4.757910 4.760415 4.762922 4.765430
## [13,] 4.771332 4.774826 4.778323 4.781823 4.785325 4.788830 4.792338 4.795848
## [14,] 4.794877 4.799376 4.803880 4.808387 4.812899 4.817415 4.821935 4.826460
## [15,] 4.818539 4.824053 4.829573 4.835099 4.840631 4.846170 4.851715 4.857267
## [16,] 4.842318 4.848856 4.855403 4.861959 4.868523 4.875097 4.881679 4.888270
## [17,] 4.866214 4.873787 4.881372 4.888968 4.896576 4.904196 4.911828 4.919472
## [18,] 4.890228 4.898846 4.907479 4.916127 4.924791 4.933470 4.942164 4.950873
## [19,] 4.914361 4.924034 4.933726 4.943438 4.953168 4.962918 4.972686 4.982474
## [20,] 4.938613 4.949351 4.960114 4.970899 4.981709 4.992541 5.003397 5.014277
## [21,] 4.962984 4.974799 4.986642 4.998514 5.010414 5.022342 5.034298 5.046283
## [22,] 4.987475 5.000377 5.013313 5.026282 5.039284 5.052320 5.065390 5.078494
## [23,] 5.012088 5.026087 5.040126 5.054204 5.068321 5.082478 5.096674 5.110909
## [24,] 5.036822 5.051929 5.067083 5.082281 5.097525 5.112815 5.128151 5.143532
## [25,] 5.061678 5.077904 5.094183 5.110514 5.126897 5.143333 5.159822 5.176363
## [26,] 5.086656 5.104013 5.121429 5.138904 5.156439 5.174034 5.191689 5.209404
## [27,] 5.111758 5.130256 5.148820 5.167452 5.186151 5.204918 5.223752 5.242655
## [28,] 5.136984 5.156633 5.176358 5.196158 5.216034 5.235986 5.256014 5.276119
## [29,] 5.162334 5.183147 5.204043 5.225024 5.246089 5.267240 5.288475 5.309796
## [30,] 5.187810 5.209796 5.231877 5.254050 5.276318 5.298680 5.321137 5.343689
## [31,] 5.213411 5.236583 5.259859 5.283238 5.306720 5.330308 5.354000 5.377797
## [32,] 5.239138 5.263508 5.287990 5.312587 5.337298 5.362124 5.387066 5.412123
## [33,] 5.264992 5.290570 5.316273 5.342100 5.368052 5.394131 5.420336 5.446669
## [34,] 5.290974 5.317772 5.344706 5.371776 5.398983 5.426329 5.453812 5.481435
## [35,] 5.317085 5.345114 5.373292 5.401618 5.430093 5.458718 5.487495 5.516423
## [36,] 5.343324 5.372597 5.402030 5.431625 5.461382 5.491301 5.521385 5.551634
## [37,] 5.369692 5.400220 5.430922 5.461799 5.492851 5.524079 5.555485 5.587070
## [38,] 5.396191 5.427986 5.459969 5.492140 5.524501 5.557052 5.589796 5.622732
## [39,] 5.422820 5.455895 5.489171 5.522650 5.556334 5.590222 5.624318 5.658622
## [40,] 5.449581 5.483947 5.518529 5.553330 5.588350 5.623591 5.659054 5.694740
## [41,] 5.476474 5.512143 5.548044 5.584180 5.620550 5.657158 5.694004 5.731090
## [42,] 5.503499 5.540484 5.577717 5.615201 5.652936 5.690925 5.729170 5.767671
## [43,] 5.530658 5.568971 5.607549 5.646395 5.685509 5.724895 5.764553 5.804486
## [44,] 5.557951 5.597604 5.637541 5.677762 5.718270 5.759067 5.800155 5.841536
## [45,] 5.585379 5.626385 5.667692 5.709303 5.751219 5.793443 5.835976 5.878822
## [46,] 5.612942 5.655314 5.698005 5.741019 5.784358 5.828024 5.872019 5.916347
## [47,] 5.640641 5.684391 5.728480 5.772912 5.817688 5.862811 5.908284 5.954110
## [48,] 5.668477 5.713618 5.759119 5.804982 5.851210 5.897806 5.944774 5.992115
## [49,] 5.696450 5.742995 5.789921 5.837230 5.884925 5.933010 5.981489 6.030363
## [50,] 5.724561 5.772523 5.820887 5.869657 5.918835 5.968425 6.018430 6.068854
## [51,] 5.752811 5.802203 5.852020 5.902264 5.952939 6.004050 6.055600 6.107592
## [52,] 5.781200 5.832036 5.883319 5.935052 5.987241 6.039888 6.092999 6.146576
## [53,] 5.809729 5.862022 5.914785 5.968023 6.021740 6.075941 6.130629 6.185810
## [54,] 5.838399 5.892162 5.946419 6.001176 6.056438 6.112208 6.168492 6.225294
## [55,] 5.867211 5.922457 5.978223 6.034514 6.091335 6.148692 6.206588 6.265030
## [56,] 5.896165 5.952908 6.010197 6.068037 6.126434 6.185393 6.244920 6.305019
## [57,] 5.925262 5.983515 6.042342 6.101747 6.161735 6.222314 6.283488 6.345264
## [58,] 5.954502 6.014280 6.074659 6.135643 6.197240 6.259455 6.322295 6.385765
## [59,] 5.983886 6.045203 6.107148 6.169728 6.232949 6.296818 6.361341 6.426526
## [60,] 6.013416 6.076285 6.139812 6.204002 6.268864 6.334404 6.400629 6.467546
## [61,] 6.043091 6.107527 6.172650 6.238467 6.304986 6.372214 6.440159 6.508828
## [62,] 6.072913 6.138929 6.205663 6.273123 6.341315 6.410249 6.479933 6.550374
## [63,] 6.102882 6.170493 6.238854 6.307971 6.377855 6.448512 6.519953 6.592185
## [64,] 6.132999 6.202220 6.272221 6.343013 6.414604 6.487004 6.560220 6.634262
## [65,] 6.163264 6.234109 6.305768 6.378250 6.451566 6.525725 6.600735 6.676609
## [66,] 6.193679 6.266162 6.339493 6.413683 6.488741 6.564677 6.641501 6.719225
## [67,] 6.224244 6.298380 6.373399 6.449312 6.526129 6.603861 6.682519 6.762114
## [68,] 6.254960 6.330764 6.407487 6.485140 6.563733 6.643280 6.723790 6.805276
## [69,] 6.285827 6.363314 6.441757 6.521166 6.601554 6.682934 6.765316 6.848714
## [70,] 6.316847 6.396032 6.476210 6.557392 6.639593 6.722824 6.807098 6.892429
## [71,] 6.348019 6.428918 6.510847 6.593820 6.677851 6.762953 6.849139 6.936423
## [72,] 6.379346 6.461972 6.545669 6.630450 6.716329 6.803321 6.891439 6.980698
## [73,] 6.410827 6.495197 6.580678 6.667284 6.755029 6.843930 6.934000 7.025256
## [74,] 6.442463 6.528593 6.615874 6.704322 6.793953 6.884781 6.976824 7.070098
## [75,] 6.474256 6.562160 6.651258 6.741566 6.833100 6.925877 7.019913 7.115226
## [76,] 6.506205 6.595900 6.686832 6.779017 6.872473 6.967217 7.063268 7.160642
## [77,] 6.538313 6.629814 6.722596 6.816676 6.912073 7.008805 7.106890 7.206349
## [78,] 6.570578 6.663902 6.758551 6.854544 6.951901 7.050640 7.150782 7.252347
## [79,] 6.603003 6.698165 6.794698 6.892622 6.991958 7.092726 7.194945 7.298638
## [80,] 6.635588 6.732604 6.831039 6.930913 7.032247 7.135062 7.239381 7.345225
## [81,] 6.668333 6.767220 6.867574 6.969415 7.072767 7.177651 7.284091 7.392109
## [82,] 6.701241 6.802015 6.904304 7.008132 7.113521 7.220495 7.329077 7.439293
## [83,] 6.734310 6.836988 6.941231 7.047064 7.154510 7.263594 7.374342 7.486778
## [84,] 6.767543 6.872141 6.978355 7.086212 7.195735 7.306951 7.419885 7.534566
## [85,] 6.800940 6.907475 7.015678 7.125577 7.237197 7.350566 7.465710 7.582659
## [86,] 6.834502 6.942990 7.053201 7.165161 7.278899 7.394441 7.511818 7.631058
## [87,] 6.868229 6.978688 7.090924 7.204965 7.320840 7.438579 7.558211 7.679767
## [88,] 6.902122 7.014570 7.128849 7.244990 7.363024 7.482980 7.604890 7.728787
## [89,] 6.936183 7.050636 7.166977 7.285238 7.405450 7.527646 7.651858 7.778120
## [90,] 6.970412 7.086887 7.205309 7.325709 7.448121 7.572578 7.699116 7.827767
## [91,] 7.004810 7.123325 7.243846 7.366405 7.491038 7.617779 7.746665 7.877732
## [92,] 7.039378 7.159951 7.282588 7.407327 7.534202 7.663250 7.794508 7.928015
## [93,] 7.074116 7.196764 7.321539 7.448476 7.577614 7.708992 7.842647 7.978619
## [94,] 7.109026 7.233767 7.360697 7.489854 7.621277 7.755007 7.891083 8.029546
## [95,] 7.144108 7.270960 7.400065 7.531462 7.665192 7.801297 7.939818 8.080799
## [96,] 7.179363 7.308345 7.439643 7.573301 7.709359 7.847863 7.988854 8.132378
## [97,] 7.214792 7.345921 7.479433 7.615372 7.753781 7.894706 8.038193 8.184287
## [98,] 7.250396 7.383691 7.519436 7.657677 7.798459 7.941830 8.087836 8.236527
## [99,] 7.286176 7.421655 7.559653 7.700217 7.843395 7.989235 8.137787 8.289101
## [,57] [,58] [,59] [,60] [,61] [,62] [,63] [,64]
## [1,] 4.435596 4.427900 4.420219 4.412550 4.404895 4.397253 4.389624 4.382009
## [2,] 4.464826 4.457997 4.451179 4.444371 4.437573 4.430786 4.424009 4.417243
## [3,] 4.494249 4.488299 4.482356 4.476421 4.470494 4.464575 4.458663 4.452760
## [4,] 4.523867 4.518806 4.513751 4.508702 4.503659 4.498621 4.493589 4.488562
## [5,] 4.553679 4.549521 4.545367 4.541216 4.537070 4.532927 4.528788 4.524652
## [6,] 4.583688 4.580445 4.577204 4.573965 4.570728 4.567494 4.564263 4.561033
## [7,] 4.613894 4.611578 4.609263 4.606950 4.604637 4.602326 4.600015 4.597706
## [8,] 4.644300 4.642924 4.641548 4.640172 4.638797 4.637422 4.636048 4.634674
## [9,] 4.674906 4.674482 4.674058 4.673634 4.673211 4.672787 4.672363 4.671939
## [10,] 4.705714 4.706255 4.706796 4.707338 4.707879 4.708421 4.708962 4.709504
## [11,] 4.736724 4.738244 4.739764 4.741284 4.742805 4.744327 4.745849 4.747371
## [12,] 4.767940 4.770450 4.772962 4.775476 4.777990 4.780506 4.783024 4.785542
## [13,] 4.799360 4.802876 4.806393 4.809914 4.813436 4.816962 4.820490 4.824021
## [14,] 4.830988 4.835521 4.840058 4.844600 4.849145 4.853695 4.858250 4.862808
## [15,] 4.862824 4.868389 4.873959 4.879536 4.885119 4.890709 4.896305 4.901908
## [16,] 4.894871 4.901480 4.908098 4.914724 4.921360 4.928005 4.934659 4.941322
## [17,] 4.927128 4.934795 4.942475 4.950167 4.957870 4.965585 4.973313 4.981052
## [18,] 4.959598 4.968338 4.977093 4.985864 4.994651 5.003452 5.012270 5.021103
## [19,] 4.992282 5.002108 5.011954 5.021819 5.031704 5.041608 5.051532 5.061475
## [20,] 5.025181 5.036108 5.047059 5.058034 5.069032 5.080055 5.091101 5.102172
## [21,] 5.058297 5.070339 5.082410 5.094509 5.106637 5.118795 5.130981 5.143196
## [22,] 5.091631 5.104802 5.118008 5.131248 5.144522 5.157830 5.171173 5.184550
## [23,] 5.125185 5.139500 5.153856 5.168251 5.182687 5.197163 5.211679 5.226236
## [24,] 5.158960 5.174434 5.189955 5.205522 5.221135 5.236796 5.252503 5.268258
## [25,] 5.192958 5.209605 5.226306 5.243061 5.259869 5.276731 5.293647 5.310618
## [26,] 5.227179 5.245015 5.262912 5.280871 5.298890 5.316971 5.335113 5.353318
## [27,] 5.261626 5.280666 5.299775 5.318953 5.338200 5.357517 5.376904 5.396361
## [28,] 5.296301 5.316560 5.336896 5.357310 5.377802 5.398373 5.419022 5.439751
## [29,] 5.331203 5.352697 5.374277 5.395944 5.417698 5.439540 5.461471 5.483489
## [30,] 5.366336 5.389080 5.411920 5.434856 5.457890 5.481022 5.504251 5.527579
## [31,] 5.401700 5.425710 5.449826 5.474049 5.498380 5.522819 5.547367 5.572024
## [32,] 5.437298 5.462589 5.487998 5.513525 5.539171 5.564936 5.590821 5.616826
## [33,] 5.473129 5.499719 5.526437 5.553285 5.580264 5.607373 5.634614 5.661988
## [34,] 5.509197 5.537101 5.565145 5.593332 5.621661 5.650134 5.678751 5.707513
## [35,] 5.545503 5.574737 5.604125 5.633668 5.663366 5.693221 5.723234 5.753405
## [36,] 5.582048 5.612629 5.643378 5.674294 5.705381 5.736637 5.768065 5.799665
## [37,] 5.618834 5.650779 5.682905 5.715214 5.747707 5.780384 5.813247 5.846297
## [38,] 5.655862 5.689188 5.722709 5.756429 5.790347 5.824465 5.858784 5.893305
## [39,] 5.693134 5.727858 5.762793 5.797941 5.833303 5.868881 5.904677 5.940690
## [40,] 5.730652 5.766790 5.803157 5.839752 5.876578 5.913637 5.950929 5.988456
## [41,] 5.768417 5.805988 5.843803 5.881865 5.920174 5.958733 5.997544 6.036607
## [42,] 5.806431 5.845452 5.884735 5.924281 5.964094 6.004174 6.044523 6.085144
## [43,] 5.844696 5.885184 5.925953 5.967004 6.008339 6.049961 6.091871 6.134072
## [44,] 5.883212 5.925186 5.967459 6.010034 6.052913 6.096097 6.139590 6.183393
## [45,] 5.921983 5.965460 6.009257 6.053375 6.097817 6.142585 6.187682 6.233111
## [46,] 5.961009 6.006008 6.051347 6.097028 6.143054 6.189428 6.236152 6.283228
## [47,] 6.000292 6.046832 6.093732 6.140996 6.188627 6.236628 6.285001 6.333748
## [48,] 6.039834 6.087932 6.136414 6.185282 6.234539 6.284188 6.334232 6.384675
## [49,] 6.079636 6.129313 6.179395 6.229886 6.280790 6.332110 6.383849 6.436011
## [50,] 6.119701 6.170974 6.222677 6.274812 6.327385 6.380398 6.433855 6.487760
## [51,] 6.160030 6.212919 6.266262 6.320063 6.374325 6.429054 6.484253 6.539925
## [52,] 6.200625 6.255149 6.310152 6.365639 6.421614 6.478081 6.535045 6.592509
## [53,] 6.241487 6.297666 6.354350 6.411544 6.469254 6.527482 6.586235 6.645517
## [54,] 6.282619 6.340472 6.398857 6.457781 6.517247 6.577260 6.637826 6.698950
## [55,] 6.324021 6.383569 6.443676 6.504350 6.565596 6.627417 6.689821 6.752813
## [56,] 6.365697 6.426958 6.488809 6.551256 6.614303 6.677957 6.742224 6.807109
## [57,] 6.407647 6.470643 6.534259 6.598500 6.663372 6.728883 6.795037 6.861842
## [58,] 6.449873 6.514625 6.580026 6.646084 6.712805 6.780196 6.848264 6.917015
## [59,] 6.492378 6.558905 6.626114 6.694012 6.762605 6.831901 6.901907 6.972631
## [60,] 6.535163 6.603487 6.672525 6.742285 6.812774 6.884000 6.955971 7.028695
## [61,] 6.578230 6.648371 6.719261 6.790906 6.863316 6.936497 7.010459 7.085209
## [62,] 6.621580 6.693561 6.766324 6.839878 6.914232 6.989394 7.065373 7.142178
## [63,] 6.665217 6.739058 6.813717 6.889203 6.965526 7.042694 7.120717 7.199605
## [64,] 6.709140 6.784864 6.861442 6.938884 7.017201 7.096401 7.176495 7.257493
## [65,] 6.753354 6.830981 6.909501 6.988923 7.069258 7.150517 7.232710 7.315847
## [66,] 6.797859 6.877412 6.957897 7.039323 7.121703 7.205046 7.289365 7.374670
## [67,] 6.842657 6.924159 7.006631 7.090087 7.174536 7.259991 7.346464 7.433967
## [68,] 6.887750 6.971223 7.055708 7.141216 7.227761 7.315355 7.404010 7.493740
## [69,] 6.933140 7.018607 7.105127 7.192714 7.281381 7.371141 7.462007 7.553993
## [70,] 6.978830 7.066313 7.154893 7.244584 7.335399 7.427352 7.520458 7.614731
## [71,] 7.024820 7.114344 7.205008 7.296828 7.389817 7.483992 7.579367 7.675958
## [72,] 7.071114 7.162701 7.255473 7.349448 7.444640 7.541064 7.638738 7.737676
## [73,] 7.117713 7.211386 7.306292 7.402448 7.499869 7.598571 7.698573 7.799891
## [74,] 7.164618 7.260403 7.357467 7.455830 7.555507 7.656517 7.758878 7.862606
## [75,] 7.211833 7.309752 7.409001 7.509597 7.611559 7.714905 7.819654 7.925826
## [76,] 7.259359 7.359437 7.460895 7.563752 7.668026 7.773738 7.880907 7.989554
## [77,] 7.307199 7.409460 7.513153 7.618297 7.724912 7.833019 7.942640 8.053794
## [78,] 7.355353 7.459823 7.565777 7.673235 7.782220 7.892753 8.004856 8.118551
## [79,] 7.403825 7.510528 7.618769 7.728570 7.839954 7.952942 8.067559 8.183828
## [80,] 7.452617 7.561578 7.672133 7.784304 7.898115 8.013590 8.130754 8.249630
## [81,] 7.501729 7.612975 7.725870 7.840440 7.956708 8.074701 8.194443 8.315961
## [82,] 7.551166 7.664721 7.779984 7.896980 8.015736 8.136278 8.258632 8.382826
## [83,] 7.600928 7.716819 7.834477 7.953929 8.075202 8.198324 8.323323 8.450228
## [84,] 7.651018 7.769271 7.889351 8.011288 8.135109 8.260843 8.388521 8.518173
## [85,] 7.701439 7.822080 7.944610 8.069060 8.195460 8.323839 8.454230 8.586663
## [86,] 7.752191 7.875247 8.000256 8.127250 8.256259 8.387316 8.520454 8.655704
## [87,] 7.803278 7.928776 8.056292 8.185859 8.317509 8.451277 8.587196 8.725301
## [88,] 7.854702 7.982669 8.112720 8.244890 8.379213 8.515725 8.654461 8.795457
## [89,] 7.906465 8.036928 8.169543 8.304347 8.441376 8.580665 8.722253 8.866177
## [90,] 7.958568 8.091556 8.226765 8.364233 8.503999 8.646100 8.790576 8.937466
## [91,] 8.011016 8.146555 8.284387 8.424551 8.567087 8.712034 8.859434 9.009327
## [92,] 8.063808 8.201928 8.342413 8.485304 8.630643 8.778471 8.928831 9.081767
## [93,] 8.116949 8.257677 8.400845 8.546495 8.694670 8.845415 8.998772 9.154789
## [94,] 8.170440 8.313805 8.459686 8.608127 8.759173 8.912869 9.069261 9.228398
## [95,] 8.224283 8.370315 8.518940 8.670204 8.824154 8.980837 9.140303 9.302600
## [96,] 8.278481 8.427209 8.578609 8.732728 8.889617 9.049324 9.211900 9.377397
## [97,] 8.333037 8.484490 8.638695 8.795703 8.955565 9.118333 9.284059 9.452797
## [98,] 8.387951 8.542159 8.699203 8.859133 9.022003 9.187868 9.356782 9.528802
## [99,] 8.443228 8.600221 8.760134 8.923020 9.088934 9.257934 9.430076 9.605418
## [,65] [,66] [,67] [,68] [,69] [,70] [,71]
## [1,] 4.374407 4.366818 4.359242 4.351679 4.344130 4.336593 4.329070
## [2,] 4.410487 4.403741 4.397005 4.390280 4.383565 4.376861 4.370166
## [3,] 4.446864 4.440976 4.435096 4.429223 4.423359 4.417502 4.411653
## [4,] 4.483541 4.478526 4.473516 4.468512 4.463513 4.458520 4.453533
## [5,] 4.520521 4.516393 4.512269 4.508149 4.504033 4.499920 4.495811
## [6,] 4.557806 4.554581 4.551358 4.548138 4.544920 4.541704 4.538490
## [7,] 4.595398 4.593091 4.590786 4.588481 4.586178 4.583876 4.581575
## [8,] 4.633301 4.631927 4.630555 4.629182 4.627811 4.626439 4.625068
## [9,] 4.671516 4.671092 4.670668 4.670245 4.669821 4.669398 4.668974
## [10,] 4.710046 4.710588 4.711129 4.711671 4.712213 4.712755 4.713297
## [11,] 4.748894 4.750417 4.751941 4.753465 4.754990 4.756516 4.758041
## [12,] 4.788062 4.790584 4.793106 4.795630 4.798155 4.800682 4.803210
## [13,] 4.827554 4.831090 4.834628 4.838169 4.841713 4.845259 4.848807
## [14,] 4.867371 4.871938 4.876509 4.881085 4.885665 4.890249 4.894838
## [15,] 4.907517 4.913132 4.918754 4.924382 4.930016 4.935657 4.941305
## [16,] 4.947993 4.954674 4.961364 4.968063 4.974771 4.981487 4.988213
## [17,] 4.988804 4.996568 5.004343 5.012131 5.019931 5.027743 5.035567
## [18,] 5.029951 5.038815 5.047695 5.056590 5.065501 5.074428 5.083370
## [19,] 5.071438 5.081420 5.091422 5.101444 5.111485 5.121546 5.131627
## [20,] 5.113266 5.124385 5.135528 5.146695 5.157887 5.169102 5.180342
## [21,] 5.155440 5.167714 5.180016 5.192348 5.204709 5.217100 5.229520
## [22,] 5.197962 5.211408 5.224890 5.238406 5.251957 5.265543 5.279164
## [23,] 5.240834 5.255472 5.270152 5.284872 5.299634 5.314436 5.329280
## [24,] 5.284060 5.299909 5.315806 5.331751 5.347743 5.363783 5.379872
## [25,] 5.327642 5.344722 5.361856 5.379045 5.396289 5.413589 5.430943
## [26,] 5.371584 5.389913 5.408305 5.426759 5.445276 5.463856 5.482500
## [27,] 5.415889 5.435487 5.455156 5.474896 5.494707 5.514591 5.534546
## [28,] 5.460558 5.481446 5.502413 5.523460 5.544588 5.565796 5.587086
## [29,] 5.505597 5.527793 5.550079 5.572455 5.594921 5.617477 5.640125
## [30,] 5.551006 5.574532 5.598158 5.621884 5.645711 5.669638 5.693667
## [31,] 5.596790 5.621667 5.646654 5.671752 5.696962 5.722284 5.747718
## [32,] 5.642952 5.669200 5.695570 5.722062 5.748678 5.775418 5.802282
## [33,] 5.689495 5.717135 5.744909 5.772819 5.800864 5.829045 5.857363
## [34,] 5.736421 5.765475 5.794676 5.824026 5.853523 5.883171 5.912968
## [35,] 5.783735 5.814224 5.844875 5.875687 5.906661 5.937799 5.969101
## [36,] 5.831438 5.863385 5.895508 5.927806 5.960281 5.992934 6.025766
## [37,] 5.879535 5.912962 5.946579 5.980387 6.014388 6.048581 6.082969
## [38,] 5.928029 5.962958 5.998093 6.033435 6.068986 6.104745 6.140716
## [39,] 5.976923 6.013377 6.050054 6.086954 6.124079 6.161431 6.199010
## [40,] 6.026220 6.064222 6.102464 6.140947 6.179673 6.218642 6.257858
## [41,] 6.075924 6.115497 6.155329 6.195419 6.235771 6.276386 6.317265
## [42,] 6.126038 6.167206 6.208651 6.250375 6.292379 6.334665 6.377235
## [43,] 6.176565 6.219352 6.262435 6.305817 6.349500 6.393485 6.437775
## [44,] 6.227508 6.271938 6.316686 6.361752 6.407140 6.452852 6.498890
## [45,] 6.278872 6.324970 6.371406 6.418183 6.465303 6.512769 6.560584
## [46,] 6.330660 6.378450 6.426600 6.475114 6.523994 6.573244 6.622865
## [47,] 6.382874 6.432381 6.482272 6.532550 6.583218 6.634279 6.685736
## [48,] 6.435520 6.486769 6.538427 6.590496 6.642980 6.695882 6.749205
## [49,] 6.488599 6.541617 6.595068 6.648956 6.703284 6.758056 6.813276
## [50,] 6.542117 6.596929 6.652200 6.707934 6.764136 6.820808 6.877955
## [51,] 6.596075 6.652708 6.709827 6.767436 6.825540 6.884142 6.943248
## [52,] 6.650479 6.708959 6.767953 6.827465 6.887501 6.948065 7.009161
## [53,] 6.705332 6.765685 6.826582 6.888027 6.950025 7.012581 7.075700
## [54,] 6.760637 6.822891 6.885719 6.949126 7.013116 7.077696 7.142870
## [55,] 6.816398 6.880581 6.945369 7.010767 7.076781 7.143416 7.210679
## [56,] 6.872619 6.938759 7.005536 7.072955 7.141023 7.209746 7.279130
## [57,] 6.929304 6.997428 7.066223 7.135694 7.205848 7.276692 7.348232
## [58,] 6.986456 7.056594 7.127436 7.198990 7.271262 7.344259 7.417990
## [59,] 7.044079 7.116260 7.189180 7.262847 7.337269 7.412454 7.488409
## [60,] 7.102178 7.176430 7.251458 7.327271 7.403876 7.481282 7.559498
## [61,] 7.160756 7.237109 7.314276 7.392266 7.471088 7.550750 7.631261
## [62,] 7.219818 7.298302 7.377639 7.457838 7.538909 7.620862 7.703705
## [63,] 7.279366 7.360011 7.441550 7.523991 7.607347 7.691625 7.776838
## [64,] 7.339406 7.422243 7.506014 7.590732 7.676405 7.763046 7.850664
## [65,] 7.399940 7.485000 7.571037 7.658064 7.746091 7.835129 7.925191
## [66,] 7.460974 7.548288 7.636624 7.725993 7.816409 7.907882 8.000426
## [67,] 7.522512 7.612112 7.702779 7.794525 7.887365 7.981311 8.076375
## [68,] 7.584557 7.676474 7.769506 7.863665 7.958966 8.055421 8.153045
## [69,] 7.647113 7.741382 7.836812 7.933419 8.031216 8.130219 8.230443
## [70,] 7.710186 7.806838 7.904701 8.003791 8.104122 8.205712 8.308575
## [71,] 7.773779 7.872847 7.973178 8.074787 8.177691 8.281906 8.387450
## [72,] 7.837896 7.939415 8.042248 8.146413 8.251927 8.358808 8.467073
## [73,] 7.902543 8.006545 8.111916 8.218674 8.326837 8.436423 8.547452
## [74,] 7.967722 8.074243 8.182188 8.291576 8.402427 8.514759 8.628594
## [75,] 8.033439 8.142513 8.253069 8.365125 8.478703 8.593823 8.710506
## [76,] 8.099698 8.211361 8.324563 8.439326 8.555671 8.673621 8.793196
## [77,] 8.166504 8.280791 8.396678 8.514186 8.633339 8.754159 8.876670
## [78,] 8.233860 8.350808 8.469416 8.589709 8.711711 8.835446 8.960938
## [79,] 8.301772 8.421417 8.542785 8.665903 8.790795 8.917487 9.046005
## [80,] 8.370245 8.492623 8.616790 8.742772 8.870597 9.000290 9.131880
## [81,] 8.439282 8.564431 8.691435 8.820323 8.951123 9.083862 9.218570
## [82,] 8.508888 8.636846 8.766727 8.898563 9.032380 9.168210 9.306083
## [83,] 8.579069 8.709873 8.842672 8.977496 9.114375 9.253341 9.394426
## [84,] 8.649828 8.783518 8.919274 9.057129 9.197114 9.339263 9.483609
## [85,] 8.721171 8.857786 8.996540 9.137468 9.280604 9.425982 9.573638
## [86,] 8.793102 8.932681 9.074476 9.218521 9.364853 9.513507 9.664521
## [87,] 8.865627 9.008210 9.153086 9.300292 9.449865 9.601845 9.756268
## [88,] 8.938750 9.084377 9.232377 9.382789 9.535650 9.691002 9.848885
## [89,] 9.012476 9.161189 9.312356 9.466017 9.622214 9.780988 9.942382
## [90,] 9.086810 9.238650 9.393027 9.549983 9.709563 9.871809 10.036766
## [91,] 9.161757 9.316766 9.474397 9.634695 9.797705 9.963473 10.132046
## [92,] 9.237322 9.395542 9.556472 9.720158 9.886647 10.055989 10.228231
## [93,] 9.313511 9.474984 9.639257 9.806379 9.976397 10.149364 10.325329
## [94,] 9.390328 9.555099 9.722760 9.893364 10.066962 10.243605 10.423348
## [95,] 9.467778 9.635890 9.806987 9.981122 10.158348 10.338722 10.522298
## [96,] 9.545868 9.717365 9.891943 10.069657 10.250565 10.434722 10.622188
## [97,] 9.624601 9.799528 9.977635 10.158978 10.343618 10.531613 10.723025
## [98,] 9.703984 9.882387 10.064069 10.249092 10.437516 10.629404 10.824820
## [99,] 9.784021 9.965946 10.151252 10.340004 10.532266 10.728103 10.927582
## [,72] [,73] [,74] [,75] [,76] [,77] [,78]
## [1,] 4.321560 4.314062 4.306578 4.299107 4.291648 4.284203 4.276770
## [2,] 4.363482 4.356808 4.350145 4.343491 4.336848 4.330215 4.323592
## [3,] 4.405811 4.399978 4.394152 4.388334 4.382523 4.376720 4.370925
## [4,] 4.448551 4.443575 4.438604 4.433639 4.428680 4.423726 4.418777
## [5,] 4.491706 4.487604 4.483507 4.479413 4.475323 4.471236 4.467153
## [6,] 4.535279 4.532070 4.528863 4.525659 4.522456 4.519257 4.516059
## [7,] 4.579275 4.576976 4.574678 4.572382 4.570087 4.567793 4.565500
## [8,] 4.623697 4.622327 4.620957 4.619588 4.618219 4.616850 4.615482
## [9,] 4.668551 4.668128 4.667704 4.667281 4.666858 4.666435 4.666011
## [10,] 4.713840 4.714382 4.714924 4.715467 4.716009 4.716551 4.717094
## [11,] 4.759568 4.761094 4.762622 4.764150 4.765678 4.767207 4.768736
## [12,] 4.805739 4.808270 4.810802 4.813335 4.815870 4.818406 4.820943
## [13,] 4.852359 4.855913 4.859469 4.863029 4.866590 4.870155 4.873722
## [14,] 4.899431 4.904028 4.908629 4.913235 4.917845 4.922460 4.927078
## [15,] 4.946959 4.952619 4.958286 4.963960 4.969640 4.975326 4.981019
## [16,] 4.994948 5.001693 5.008446 5.015208 5.021980 5.028760 5.035550
## [17,] 5.043403 5.051252 5.059113 5.066986 5.074871 5.082769 5.090678
## [18,] 5.092328 5.101302 5.110292 5.119298 5.128319 5.137357 5.146410
## [19,] 5.141728 5.151849 5.161990 5.172150 5.182331 5.192531 5.202752
## [20,] 5.191607 5.202896 5.214210 5.225548 5.236911 5.248298 5.259711
## [21,] 5.241970 5.254449 5.266958 5.279497 5.292066 5.304664 5.317293
## [22,] 5.292821 5.306513 5.320240 5.334003 5.347802 5.361636 5.375506
## [23,] 5.344166 5.359093 5.374061 5.389072 5.404125 5.419219 5.434356
## [24,] 5.396008 5.412193 5.428427 5.444709 5.461041 5.477421 5.493850
## [25,] 5.448354 5.465820 5.483343 5.500921 5.518556 5.536247 5.553996
## [26,] 5.501207 5.519979 5.538814 5.557713 5.576677 5.595706 5.614800
## [27,] 5.554573 5.574673 5.594846 5.615092 5.635411 5.655803 5.676269
## [28,] 5.608457 5.629910 5.651445 5.673063 5.694763 5.716546 5.738412
## [29,] 5.662864 5.685694 5.708617 5.731632 5.754740 5.777941 5.801235
## [30,] 5.717798 5.742031 5.766367 5.790806 5.815348 5.839995 5.864746
## [31,] 5.773265 5.798926 5.824701 5.850591 5.876595 5.902716 5.928952
## [32,] 5.829271 5.856385 5.883626 5.910993 5.938488 5.966110 5.993861
## [33,] 5.885819 5.914413 5.943146 5.972019 6.001032 6.030185 6.059481
## [34,] 5.942916 5.973016 6.003269 6.033675 6.064234 6.094949 6.125819
## [35,] 6.000567 6.032200 6.064000 6.095967 6.128102 6.160408 6.192883
## [36,] 6.058778 6.091970 6.125345 6.158902 6.192643 6.226569 6.260681
## [37,] 6.117553 6.152333 6.187311 6.222487 6.257864 6.293442 6.329222
## [38,] 6.176898 6.213293 6.249903 6.286729 6.323772 6.361033 6.398513
## [39,] 6.236819 6.274858 6.313129 6.351634 6.390374 6.429349 6.468563
## [40,] 6.297321 6.337033 6.376995 6.417209 6.457677 6.498400 6.539379
## [41,] 6.358410 6.399823 6.441506 6.483461 6.525689 6.568192 6.610971
## [42,] 6.420092 6.463236 6.506671 6.550397 6.594417 6.638733 6.683347
## [43,] 6.482372 6.527277 6.572494 6.618024 6.663869 6.710032 6.756515
## [44,] 6.545256 6.591953 6.638983 6.686349 6.734053 6.782097 6.830484
## [45,] 6.608750 6.657270 6.706145 6.755380 6.804976 6.854936 6.905263
## [46,] 6.672860 6.723233 6.773987 6.825123 6.876645 6.928557 6.980860
## [47,] 6.737592 6.789851 6.842514 6.895586 6.949070 7.002969 7.057285
## [48,] 6.802952 6.857128 6.911735 6.966777 7.022257 7.078180 7.134547
## [49,] 6.868946 6.925072 6.981656 7.038703 7.096216 7.154198 7.212655
## [50,] 6.935581 6.993689 7.052285 7.111371 7.170953 7.231033 7.291617
## [51,] 7.002861 7.062987 7.123628 7.184790 7.246477 7.308694 7.371445
## [52,] 7.070795 7.132970 7.195693 7.258966 7.322797 7.387188 7.452146
## [53,] 7.139387 7.203648 7.268486 7.333909 7.399920 7.466525 7.533730
## [54,] 7.208645 7.275025 7.342017 7.409625 7.477856 7.546715 7.616208
## [55,] 7.278575 7.347110 7.416291 7.486123 7.556612 7.627766 7.699589
## [56,] 7.349183 7.419909 7.491316 7.563410 7.636198 7.709687 7.783883
## [57,] 7.420476 7.493429 7.567100 7.641496 7.716622 7.792488 7.869099
## [58,] 7.492460 7.567678 7.643651 7.720387 7.797894 7.876178 7.955248
## [59,] 7.565143 7.642663 7.720977 7.800093 7.880021 7.960767 8.042341
## [60,] 7.638531 7.718390 7.799085 7.880623 7.963013 8.046265 8.130387
## [61,] 7.712631 7.794868 7.877982 7.961983 8.046879 8.132680 8.219397
## [62,] 7.787449 7.872104 7.957678 8.044183 8.131629 8.220024 8.309381
## [63,] 7.862994 7.950105 8.038181 8.127232 8.217271 8.308306 8.400351
## [64,] 7.939271 8.028879 8.119497 8.211139 8.303815 8.397536 8.492316
## [65,] 8.016289 8.108433 8.201637 8.295912 8.391270 8.487725 8.585288
## [66,] 8.094053 8.188776 8.284607 8.381559 8.479647 8.578882 8.679278
## [67,] 8.172572 8.269914 8.368416 8.468092 8.568954 8.671018 8.774297
## [68,] 8.251852 8.351857 8.453074 8.555517 8.659202 8.764143 8.870357
## [69,] 8.331902 8.434612 8.538588 8.643845 8.750400 8.858269 8.967468
## [70,] 8.412728 8.518186 8.624966 8.733085 8.842559 8.953406 9.065642
## [71,] 8.494338 8.602589 8.712219 8.823247 8.935689 9.049564 9.164891
## [72,] 8.576740 8.687828 8.800355 8.914339 9.029799 9.146755 9.265226
## [73,] 8.659941 8.773911 8.889382 9.006371 9.124901 9.244990 9.366660
## [74,] 8.743950 8.860848 8.979309 9.099354 9.221004 9.344280 9.469204
## [75,] 8.828773 8.948646 9.070147 9.193297 9.318119 9.444636 9.572871
## [76,] 8.914419 9.037314 9.161903 9.288209 9.416257 9.546070 9.677673
## [77,] 9.000896 9.126860 9.254587 9.384102 9.515429 9.648594 9.783622
## [78,] 9.088212 9.217294 9.348210 9.480984 9.615645 9.752218 9.890732
## [79,] 9.176375 9.308624 9.442779 9.578867 9.716917 9.856956 9.999013
## [80,] 9.265393 9.400859 9.538305 9.677760 9.819255 9.962818 10.108481
## [81,] 9.355275 9.494007 9.634797 9.777675 9.922671 10.069818 10.219146
## [82,] 9.446029 9.588079 9.732266 9.878621 10.027176 10.177966 10.331024
## [83,] 9.537663 9.683083 9.830720 9.980608 10.132782 10.287276 10.444126
## [84,] 9.630186 9.779028 9.930171 10.083649 10.239500 10.397760 10.558466
## [85,] 9.723606 9.875924 10.030627 10.187754 10.347342 10.509431 10.674058
## [86,] 9.817933 9.973779 10.132100 10.292934 10.456320 10.622300 10.790915
## [87,] 9.913175 10.072605 10.234599 10.399199 10.566446 10.736383 10.909052
## [88,] 10.009340 10.172410 10.338136 10.506561 10.677731 10.851690 11.028482
## [89,] 10.106439 10.273203 10.442719 10.615032 10.790189 10.968235 11.149220
## [90,] 10.204480 10.374996 10.548361 10.724623 10.903831 11.086033 11.271280
## [91,] 10.303471 10.477797 10.655071 10.835345 11.018669 11.205095 11.394675
## [92,] 10.403423 10.581616 10.762861 10.947211 11.134718 11.325437 11.519422
## [93,] 10.504345 10.686464 10.871741 11.060231 11.251988 11.447070 11.645534
## [94,] 10.606245 10.792351 10.981723 11.174418 11.370494 11.570010 11.773027
## [95,] 10.709134 10.899288 11.092818 11.289784 11.490247 11.694270 11.901916
## [96,] 10.813021 11.007284 11.205036 11.406341 11.611262 11.819865 12.032216
## [97,] 10.917916 11.116350 11.318389 11.524101 11.733552 11.946809 12.163942
## [98,] 11.023829 11.226496 11.432890 11.643077 11.857129 12.075116 12.297111
## [99,] 11.130769 11.337734 11.548548 11.763282 11.982008 12.204801 12.431737
## [,79] [,80] [,81] [,82] [,83] [,84] [,85]
## [1,] 4.269351 4.261944 4.254550 4.247169 4.239801 4.232445 4.225103
## [2,] 4.316979 4.310376 4.303783 4.297201 4.290628 4.284066 4.277513
## [3,] 4.365138 4.359358 4.353586 4.347822 4.342065 4.336316 4.330574
## [4,] 4.413834 4.408897 4.403965 4.399039 4.394118 4.389203 4.384293
## [5,] 4.463074 4.458999 4.454927 4.450860 4.446795 4.442735 4.438678
## [6,] 4.512863 4.509670 4.506479 4.503291 4.500104 4.496920 4.493738
## [7,] 4.563208 4.560917 4.558628 4.556339 4.554052 4.551766 4.549481
## [8,] 4.614114 4.612747 4.611380 4.610013 4.608647 4.607281 4.605916
## [9,] 4.665588 4.665165 4.664742 4.664319 4.663896 4.663473 4.663050
## [10,] 4.717637 4.718179 4.718722 4.719265 4.719808 4.720350 4.720893
## [11,] 4.770266 4.771796 4.773326 4.774858 4.776389 4.777922 4.779454
## [12,] 4.823482 4.826022 4.828563 4.831105 4.833649 4.836195 4.838741
## [13,] 4.877291 4.880864 4.884438 4.888016 4.891596 4.895179 4.898764
## [14,] 4.931701 4.936329 4.940961 4.945597 4.950237 4.954882 4.959531
## [15,] 4.986718 4.992424 4.998137 5.003856 5.009581 5.015313 5.021052
## [16,] 5.042349 5.049157 5.055975 5.062801 5.069637 5.076482 5.083336
## [17,] 5.098601 5.106535 5.114482 5.122441 5.130413 5.138397 5.146393
## [18,] 5.155479 5.164565 5.173666 5.182783 5.191917 5.201066 5.210232
## [19,] 5.212993 5.223254 5.233535 5.243836 5.254158 5.264500 5.274863
## [20,] 5.271148 5.282610 5.294097 5.305609 5.317146 5.328708 5.340295
## [21,] 5.329952 5.342641 5.355360 5.368109 5.380889 5.393699 5.406539
## [22,] 5.389412 5.403353 5.417331 5.431345 5.445395 5.459482 5.473605
## [23,] 5.449535 5.464756 5.480020 5.495326 5.510676 5.526068 5.541503
## [24,] 5.510329 5.526857 5.543434 5.560061 5.576739 5.593466 5.610243
## [25,] 5.571801 5.589663 5.607582 5.625559 5.643593 5.661686 5.679836
## [26,] 5.633958 5.653183 5.672472 5.691828 5.711250 5.730737 5.750292
## [27,] 5.696810 5.717424 5.738114 5.758878 5.779717 5.800632 5.821622
## [28,] 5.760362 5.782396 5.804514 5.826717 5.849005 5.871378 5.893837
## [29,] 5.824623 5.848106 5.871684 5.895356 5.919124 5.942987 5.966947
## [30,] 5.889602 5.914563 5.939630 5.964803 5.990083 6.015470 6.040965
## [31,] 5.955305 5.981775 6.008363 6.035069 6.061893 6.088837 6.115901
## [32,] 6.021741 6.049751 6.077891 6.106162 6.134564 6.163099 6.191766
## [33,] 6.088918 6.118499 6.148223 6.178092 6.208106 6.238266 6.268572
## [34,] 6.156845 6.188029 6.219370 6.250870 6.282530 6.314350 6.346331
## [35,] 6.225529 6.258348 6.291340 6.324505 6.357846 6.391362 6.425055
## [36,] 6.294980 6.329467 6.364142 6.399008 6.434065 6.469313 6.504755
## [37,] 6.365206 6.401394 6.437788 6.474388 6.511197 6.548215 6.585444
## [38,] 6.436215 6.474138 6.512285 6.550657 6.589254 6.628080 6.667134
## [39,] 6.508016 6.547709 6.587644 6.627823 6.668247 6.708918 6.749837
## [40,] 6.580618 6.622116 6.663876 6.705899 6.748187 6.790742 6.833566
## [41,] 6.654030 6.697368 6.740989 6.784895 6.829086 6.873565 6.918333
## [42,] 6.728261 6.773476 6.818995 6.864821 6.910954 6.957397 7.004152
## [43,] 6.803320 6.850449 6.897904 6.945688 6.993803 7.042252 7.091036
## [44,] 6.879216 6.928296 6.977726 7.027508 7.077646 7.128142 7.178997
## [45,] 6.955959 7.007028 7.058471 7.110292 7.162494 7.215079 7.268050
## [46,] 7.033558 7.086654 7.140151 7.194052 7.248359 7.303076 7.358207
## [47,] 7.112023 7.167186 7.222776 7.278797 7.335253 7.392147 7.449483
## [48,] 7.191363 7.248632 7.306357 7.364542 7.423190 7.482305 7.541890
## [49,] 7.271589 7.331004 7.390905 7.451296 7.512180 7.573561 7.635444
## [50,] 7.352709 7.414313 7.476432 7.539072 7.602237 7.665931 7.730159
## [51,] 7.434734 7.498567 7.562949 7.627882 7.693374 7.759428 7.826048
## [52,] 7.517675 7.583780 7.650466 7.717739 7.785603 7.854064 7.923127
## [53,] 7.601540 7.669960 7.738996 7.808654 7.878938 7.949855 8.021410
## [54,] 7.686341 7.757120 7.828551 7.900640 7.973392 8.046814 8.120913
## [55,] 7.772089 7.845271 7.919142 7.993709 8.068978 8.144956 8.221649
## [56,] 7.858792 7.934423 8.010782 8.087875 8.165710 8.244295 8.323636
## [57,] 7.946463 8.024588 8.103482 8.183150 8.263602 8.344845 8.426887
## [58,] 8.035112 8.115778 8.197254 8.279548 8.362668 8.446622 8.531419
## [59,] 8.124750 8.208005 8.292112 8.377081 8.462920 8.549640 8.637248
## [60,] 8.215388 8.301279 8.388067 8.475763 8.564375 8.653914 8.744389
## [61,] 8.307038 8.395613 8.485133 8.575607 8.667046 8.759460 8.852860
## [62,] 8.399709 8.491019 8.583322 8.676628 8.770948 8.866294 8.962676
## [63,] 8.493415 8.587510 8.682647 8.778838 8.876096 8.974430 9.073854
## [64,] 8.588165 8.685096 8.783122 8.882253 8.982504 9.083885 9.186412
## [65,] 8.683973 8.783792 8.884759 8.986886 9.090187 9.194676 9.300365
## [66,] 8.780850 8.883610 8.987572 9.092752 9.199162 9.306817 9.415732
## [67,] 8.878807 8.984561 9.091575 9.199864 9.309443 9.420326 9.532531
## [68,] 8.977857 9.086660 9.196782 9.308239 9.421046 9.535220 9.650778
## [69,] 9.078012 9.189919 9.303206 9.417890 9.533987 9.651515 9.770492
## [70,] 9.179285 9.294352 9.410862 9.528832 9.648281 9.769228 9.891691
## [71,] 9.281687 9.399971 9.519763 9.641082 9.763947 9.888377 10.014393
## [72,] 9.385231 9.506791 9.629925 9.754654 9.880998 10.008979 10.138618
## [73,] 9.489931 9.614824 9.741361 9.869564 9.999453 10.131052 10.264383
## [74,] 9.595799 9.724085 9.854087 9.985827 10.119328 10.254614 10.391708
## [75,] 9.702847 9.834588 9.968117 10.103460 10.240640 10.379683 10.520613
## [76,] 9.811090 9.946346 10.083467 10.222479 10.363406 10.506277 10.651117
## [77,] 9.920541 10.059375 10.200152 10.342899 10.487645 10.634415 10.783240
## [78,] 10.031212 10.173688 10.318187 10.464739 10.613372 10.764116 10.917002
## [79,] 10.143118 10.289300 10.437588 10.588013 10.740607 10.895399 11.052423
## [80,] 10.256273 10.406225 10.558371 10.712740 10.869367 11.028283 11.189523
## [81,] 10.370689 10.524480 10.680551 10.838936 10.999670 11.162788 11.328325
## [82,] 10.486383 10.644078 10.804145 10.966619 11.131536 11.298933 11.468848
## [83,] 10.603367 10.765035 10.929169 11.095806 11.264983 11.436739 11.611114
## [84,] 10.721655 10.887367 11.055640 11.226514 11.400029 11.576226 11.755145
## [85,] 10.841264 11.011089 11.183575 11.358762 11.536694 11.717413 11.900963
## [86,] 10.962207 11.136217 11.312990 11.492569 11.674998 11.860323 12.048590
## [87,] 11.084499 11.262767 11.443903 11.627951 11.814960 12.004976 12.198048
## [88,] 11.208155 11.390755 11.576330 11.764928 11.956599 12.151392 12.349359
## [89,] 11.333191 11.520198 11.710290 11.903519 12.099937 12.299595 12.502548
## [90,] 11.459622 11.651111 11.845800 12.043742 12.244992 12.449605 12.657637
## [91,] 11.587463 11.783512 11.982878 12.185618 12.391787 12.601445 12.814650
## [92,] 11.716730 11.917418 12.121543 12.329164 12.540342 12.755137 12.973610
## [93,] 11.847439 12.052845 12.261812 12.474402 12.690677 12.910703 13.134543
## [94,] 11.979607 12.189811 12.403704 12.621350 12.842815 13.068166 13.297471
## [95,] 12.113249 12.328334 12.547238 12.770030 12.996777 13.227550 13.462421
## [96,] 12.248382 12.468431 12.692434 12.920461 13.152584 13.388878 13.629417
## [97,] 12.385022 12.610120 12.839309 13.072664 13.310259 13.552173 13.798484
## [98,] 12.523187 12.753419 12.987884 13.226659 13.469825 13.717460 13.969649
## [99,] 12.662893 12.898347 13.138178 13.382470 13.631303 13.884763 14.142936
## [,86] [,87] [,88] [,89] [,90] [,91] [,92]
## [1,] 4.217773 4.210455 4.203151 4.195859 4.188580 4.181313 4.174059
## [2,] 4.270971 4.264438 4.257916 4.251404 4.244901 4.238409 4.231926
## [3,] 4.324840 4.319114 4.313395 4.307684 4.301980 4.296284 4.290595
## [4,] 4.379389 4.374490 4.369596 4.364709 4.359826 4.354949 4.350078
## [5,] 4.434625 4.430576 4.426530 4.422488 4.418450 4.414416 4.410385
## [6,] 4.490559 4.487381 4.484206 4.481033 4.477863 4.474694 4.471528
## [7,] 4.547198 4.544915 4.542633 4.540353 4.538074 4.535796 4.533519
## [8,] 4.604551 4.603186 4.601822 4.600458 4.599095 4.597732 4.596369
## [9,] 4.662627 4.662205 4.661782 4.661359 4.660936 4.660514 4.660091
## [10,] 4.721437 4.721980 4.722523 4.723066 4.723609 4.724153 4.724696
## [11,] 4.780987 4.782521 4.784055 4.785590 4.787125 4.788661 4.790197
## [12,] 4.841289 4.843839 4.846389 4.848941 4.851495 4.854049 4.856606
## [13,] 4.902352 4.905943 4.909536 4.913132 4.916730 4.920331 4.923935
## [14,] 4.964185 4.968843 4.973505 4.978172 4.982843 4.987518 4.992198
## [15,] 5.026797 5.032549 5.038308 5.044072 5.049844 5.055622 5.061407
## [16,] 5.090200 5.097072 5.103954 5.110846 5.117746 5.124656 5.131576
## [17,] 5.154402 5.162423 5.170457 5.178503 5.186562 5.194633 5.202717
## [18,] 5.219414 5.228611 5.237826 5.247056 5.256303 5.265566 5.274845
## [19,] 5.285245 5.295649 5.306072 5.316516 5.326981 5.337467 5.347973
## [20,] 5.351907 5.363545 5.375208 5.386896 5.398610 5.410349 5.422114
## [21,] 5.419410 5.432312 5.445245 5.458208 5.471202 5.484227 5.497283
## [22,] 5.487765 5.501961 5.516194 5.530464 5.544770 5.559114 5.573495
## [23,] 5.556981 5.572503 5.588068 5.603676 5.619328 5.635023 5.650763
## [24,] 5.627071 5.643949 5.660878 5.677857 5.694888 5.711969 5.729102
## [25,] 5.698044 5.716311 5.734636 5.753021 5.771464 5.789966 5.808527
## [26,] 5.769913 5.789601 5.809356 5.829179 5.849069 5.869027 5.889054
## [27,] 5.842688 5.863831 5.885050 5.906346 5.927718 5.949169 5.970696
## [28,] 5.916381 5.939012 5.961729 5.984534 6.007425 6.030404 6.053471
## [29,] 5.991004 6.015157 6.039408 6.063757 6.088204 6.112749 6.137393
## [30,] 6.066568 6.092279 6.118099 6.144029 6.170068 6.196218 6.222479
## [31,] 6.143084 6.170389 6.197815 6.225363 6.253034 6.280827 6.308744
## [32,] 6.220566 6.249501 6.278570 6.307774 6.337115 6.366591 6.396205
## [33,] 6.299026 6.329627 6.360377 6.391277 6.422326 6.453527 6.484879
## [34,] 6.378474 6.410780 6.443250 6.475884 6.508684 6.541649 6.574782
## [35,] 6.458925 6.492974 6.527203 6.561612 6.596202 6.630975 6.665931
## [36,] 6.540391 6.576222 6.612250 6.648474 6.684898 6.721520 6.758344
## [37,] 6.622884 6.660537 6.698404 6.736487 6.774786 6.813302 6.852038
## [38,] 6.706418 6.745933 6.785682 6.825664 6.865882 6.906338 6.947031
## [39,] 6.791005 6.832424 6.874096 6.916022 6.958204 7.000643 7.043341
## [40,] 6.876659 6.920024 6.963663 7.007576 7.051767 7.096236 7.140986
## [41,] 6.963393 7.008747 7.054396 7.100343 7.146588 7.193135 7.239985
## [42,] 7.051222 7.098608 7.146312 7.194337 7.242684 7.291357 7.340356
## [43,] 7.140158 7.189620 7.239425 7.289575 7.340073 7.390920 7.442119
## [44,] 7.230216 7.281800 7.333752 7.386074 7.438770 7.491842 7.545293
## [45,] 7.321410 7.375161 7.429307 7.483851 7.538795 7.594143 7.649897
## [46,] 7.413754 7.469720 7.526108 7.582922 7.640165 7.697840 7.755951
## [47,] 7.507262 7.565490 7.624170 7.683305 7.742898 7.802954 7.863475
## [48,] 7.601951 7.662489 7.723510 7.785016 7.847013 7.909503 7.972491
## [49,] 7.697833 7.760731 7.824144 7.888074 7.952527 8.017507 8.083017
## [50,] 7.794925 7.860233 7.926089 7.992496 8.059460 8.126985 8.195076
## [51,] 7.893241 7.961011 8.029362 8.098301 8.167831 8.237959 8.308688
## [52,] 7.992798 8.063081 8.133982 8.205506 8.277659 8.350447 8.423875
## [53,] 8.093610 8.166459 8.239964 8.314130 8.388964 8.464472 8.540659
## [54,] 8.195693 8.271163 8.347327 8.424193 8.501766 8.580054 8.659063
## [55,] 8.299065 8.377209 8.456089 8.535712 8.616085 8.697214 8.779107
## [56,] 8.403740 8.484615 8.566268 8.648708 8.731940 8.815974 8.900816
## [57,] 8.509735 8.593398 8.677883 8.763199 8.849354 8.936355 9.024212
## [58,] 8.617067 8.703575 8.790952 8.879206 8.968346 9.058381 9.149319
## [59,] 8.725753 8.815166 8.905494 8.996749 9.088938 9.182072 9.276161
## [60,] 8.835810 8.928187 9.021529 9.115848 9.211152 9.307453 9.404761
## [61,] 8.947255 9.042657 9.139076 9.236523 9.335009 9.434546 9.535143
## [62,] 9.060106 9.158595 9.258154 9.358796 9.460532 9.563374 9.667333
## [63,] 9.174380 9.276019 9.378784 9.482688 9.587742 9.693961 9.801356
## [64,] 9.290095 9.394948 9.500985 9.608219 9.716663 9.826331 9.937237
## [65,] 9.407270 9.515403 9.624779 9.735413 9.847318 9.960509 10.075002
## [66,] 9.525922 9.637402 9.750186 9.864290 9.979729 10.096519 10.214676
## [67,] 9.646072 9.760965 9.877227 9.994873 10.113921 10.234387 10.356287
## [68,] 9.767736 9.886112 10.005923 10.127185 10.249917 10.374136 10.499861
## [69,] 9.890936 10.012864 10.136295 10.261248 10.387742 10.515795 10.645426
## [70,] 10.015689 10.141241 10.268367 10.397087 10.527420 10.659387 10.793008
## [71,] 10.142015 10.271264 10.402159 10.534723 10.668976 10.804940 10.942637
## [72,] 10.269935 10.402954 10.537695 10.674182 10.812436 10.952481 11.094340
## [73,] 10.399469 10.536332 10.674997 10.815486 10.957825 11.102036 11.248146
## [74,] 10.530636 10.671420 10.814087 10.958661 11.105168 11.253634 11.404084
## [75,] 10.663457 10.808241 10.954990 11.103732 11.254493 11.407302 11.562185
## [76,] 10.797954 10.946815 11.097729 11.250723 11.405826 11.563068 11.722477
## [77,] 10.934147 11.087167 11.242328 11.399660 11.559194 11.720960 11.884991
## [78,] 11.072058 11.229318 11.388810 11.550568 11.714624 11.881009 12.049758
## [79,] 11.211709 11.373291 11.537202 11.703474 11.872144 12.043244 12.216810
## [80,] 11.353121 11.519110 11.687526 11.858405 12.031782 12.207694 12.386177
## [81,] 11.496316 11.666799 11.839810 12.015386 12.193566 12.374389 12.557893
## [82,] 11.641318 11.816381 11.994077 12.174446 12.357526 12.543360 12.731989
## [83,] 11.788148 11.967881 12.150355 12.335611 12.523691 12.714639 12.908498
## [84,] 11.936831 12.121324 12.308669 12.498909 12.692090 12.888257 13.087455
## [85,] 12.087388 12.276734 12.469046 12.664370 12.862753 13.064245 13.268893
## [86,] 12.239845 12.434136 12.631512 12.832020 13.035712 13.242636 13.452845
## [87,] 12.394225 12.593557 12.796095 13.001890 13.210995 13.423464 13.639349
## [88,] 12.550552 12.755022 12.962823 13.174009 13.388636 13.606760 13.828437
## [89,] 12.708850 12.918556 13.131723 13.348406 13.568666 13.792559 14.020148
## [90,] 12.869145 13.084188 13.302823 13.525112 13.751116 13.980896 14.214516
## [91,] 13.031462 13.251943 13.476153 13.704158 13.936019 14.171804 14.411578
## [92,] 13.195826 13.421848 13.651742 13.885573 14.123409 14.365319 14.611373
## [93,] 13.362264 13.593933 13.829618 14.069390 14.313319 14.561477 14.813937
## [94,] 13.530800 13.768223 14.009812 14.255640 14.505782 14.760313 15.019310
## [95,] 13.701462 13.944748 14.192354 14.444356 14.700833 14.961864 15.227530
## [96,] 13.874277 14.123537 14.377274 14.635570 14.898507 15.166167 15.438636
## [97,] 14.049272 14.304617 14.564604 14.829316 15.098839 15.373260 15.652669
## [98,] 14.226473 14.488020 14.754374 15.025626 15.301864 15.583181 15.869669
## [99,] 14.405910 14.673773 14.946617 15.224535 15.507620 15.795968 16.089678
## [,93] [,94] [,95] [,96] [,97] [,98] [,99]
## [1,] 4.166818 4.159589 4.152372 4.145169 4.137977 4.130798 4.123632
## [2,] 4.225453 4.218990 4.212538 4.206094 4.199661 4.193238 4.186824
## [3,] 4.284914 4.279241 4.273574 4.267916 4.262265 4.256621 4.250985
## [4,] 4.345212 4.340351 4.335496 4.330646 4.325802 4.320963 4.316129
## [5,] 4.406358 4.402334 4.398314 4.394298 4.390286 4.386277 4.382272
## [6,] 4.468364 4.465203 4.462043 4.458886 4.455731 4.452578 4.449428
## [7,] 4.531243 4.528969 4.526695 4.524423 4.522152 4.519882 4.517613
## [8,] 4.595007 4.593645 4.592284 4.590923 4.589563 4.588202 4.586843
## [9,] 4.659668 4.659246 4.658823 4.658401 4.657978 4.657556 4.657134
## [10,] 4.725240 4.725783 4.726327 4.726870 4.727414 4.727958 4.728502
## [11,] 4.791733 4.793270 4.794808 4.796346 4.797885 4.799424 4.800963
## [12,] 4.859163 4.861722 4.864282 4.866843 4.869406 4.871970 4.874536
## [13,] 4.927541 4.931150 4.934762 4.938376 4.941993 4.945613 4.949235
## [14,] 4.996882 5.001571 5.006264 5.010961 5.015663 5.020369 5.025080
## [15,] 5.067198 5.072996 5.078801 5.084612 5.090430 5.096255 5.102086
## [16,] 5.138504 5.145442 5.152390 5.159346 5.166312 5.173288 5.180273
## [17,] 5.210814 5.218923 5.227044 5.235179 5.243326 5.251485 5.259658
## [18,] 5.284141 5.293453 5.302781 5.312126 5.321487 5.330865 5.340259
## [19,] 5.358499 5.369047 5.379615 5.390204 5.400814 5.411444 5.422096
## [20,] 5.433904 5.445720 5.457562 5.469429 5.481323 5.493242 5.505187
## [21,] 5.510371 5.523489 5.536638 5.549819 5.563032 5.576275 5.589551
## [22,] 5.587913 5.602368 5.616861 5.631391 5.645959 5.660564 5.675207
## [23,] 5.666546 5.682374 5.698245 5.714162 5.730122 5.746127 5.762177
## [24,] 5.746286 5.763522 5.780809 5.798149 5.815540 5.832983 5.850479
## [25,] 5.827148 5.845829 5.864570 5.883370 5.902231 5.921153 5.940135
## [26,] 5.909148 5.929311 5.949543 5.969844 5.990215 6.010654 6.031164
## [27,] 5.992302 6.013986 6.035748 6.057590 6.079510 6.101509 6.123588
## [28,] 6.076626 6.099870 6.123203 6.146624 6.170136 6.193737 6.217429
## [29,] 6.162137 6.186980 6.211924 6.236968 6.262113 6.287359 6.312708
## [30,] 6.248851 6.275335 6.301931 6.328639 6.355461 6.382397 6.409447
## [31,] 6.336785 6.364951 6.393241 6.421658 6.450201 6.478871 6.507668
## [32,] 6.425957 6.455846 6.485875 6.516044 6.546353 6.576803 6.607394
## [33,] 6.516383 6.548040 6.579852 6.611817 6.643938 6.676215 6.708649
## [34,] 6.608082 6.641551 6.675189 6.708998 6.742978 6.777130 6.811456
## [35,] 6.701071 6.736397 6.771908 6.807607 6.843495 6.879571 6.915837
## [36,] 6.795369 6.832597 6.870029 6.907666 6.945509 6.983560 7.021819
## [37,] 6.890994 6.930171 6.969571 7.009195 7.049045 7.089121 7.129425
## [38,] 6.987964 7.029139 7.070556 7.112217 7.154124 7.196277 7.238679
## [39,] 7.086299 7.129520 7.173004 7.216753 7.260769 7.305053 7.349608
## [40,] 7.186018 7.231334 7.276936 7.322825 7.369004 7.415474 7.462237
## [41,] 7.287140 7.334603 7.382374 7.430457 7.478852 7.527563 7.576592
## [42,] 7.389685 7.439346 7.489340 7.539670 7.590338 7.641347 7.692699
## [43,] 7.493673 7.545585 7.597856 7.650488 7.703486 7.756851 7.810585
## [44,] 7.599125 7.653341 7.707944 7.762936 7.818321 7.874100 7.930278
## [45,] 7.706060 7.762636 7.819627 7.877036 7.934867 7.993122 8.051805
## [46,] 7.814500 7.873491 7.932928 7.992813 8.053151 8.113943 8.175195
## [47,] 7.924466 7.985930 8.047871 8.110292 8.173197 8.236591 8.300475
## [48,] 8.035980 8.099975 8.164479 8.229498 8.295034 8.361092 8.427676
## [49,] 8.149063 8.215648 8.282777 8.350455 8.418686 8.487475 8.556825
## [50,] 8.263737 8.332973 8.402790 8.473191 8.544182 8.615768 8.687954
## [51,] 8.380025 8.451974 8.524541 8.597731 8.671549 8.746001 8.821092
## [52,] 8.497949 8.572674 8.648056 8.724101 8.800814 8.878202 8.956271
## [53,] 8.617532 8.695097 8.773360 8.852328 8.932006 9.012402 9.093521
## [54,] 8.738799 8.819269 8.900481 8.982440 9.065154 9.148630 9.232874
## [55,] 8.861772 8.945214 9.029443 9.114465 9.200287 9.286917 9.374363
## [56,] 8.986475 9.072958 9.160274 9.248430 9.337434 9.427294 9.518020
## [57,] 9.112933 9.202526 9.293000 9.384364 9.476625 9.569794 9.663878
## [58,] 9.241171 9.333945 9.427650 9.522296 9.617892 9.714447 9.811972
## [59,] 9.371213 9.467240 9.564250 9.662255 9.761264 9.861287 9.962335
## [60,] 9.503086 9.602438 9.702830 9.804271 9.906773 10.010347 10.115003
## [61,] 9.636813 9.739568 9.843418 9.948375 10.054452 10.161659 10.270010
## [62,] 9.772423 9.878656 9.986043 10.094597 10.204332 10.315259 10.427392
## [63,] 9.909941 10.019730 10.130734 10.242968 10.356446 10.471180 10.587186
## [64,] 10.049395 10.162818 10.277522 10.393520 10.510827 10.629459 10.749429
## [65,] 10.190810 10.307950 10.426436 10.546285 10.667510 10.790130 10.914158
## [66,] 10.334216 10.455155 10.577509 10.701295 10.826529 10.953229 11.081412
## [67,] 10.479640 10.604461 10.730770 10.858583 10.987918 11.118794 11.251229
## [68,] 10.627110 10.755900 10.886252 11.018183 11.151713 11.286861 11.423648
## [69,] 10.776655 10.909502 11.043987 11.180129 11.317950 11.457469 11.598709
## [70,] 10.928305 11.065297 11.204007 11.344455 11.486664 11.630656 11.776453
## [71,] 11.082089 11.223317 11.366346 11.511197 11.657894 11.806461 11.956921
## [72,] 11.238036 11.383594 11.531037 11.680389 11.831676 11.984923 12.140154
## [73,] 11.396179 11.546159 11.698114 11.852068 12.008049 12.166082 12.326195
## [74,] 11.556546 11.711046 11.867612 12.026271 12.187051 12.349980 12.515088
## [75,] 11.719171 11.878288 12.039566 12.203034 12.368721 12.536658 12.706875
## [76,] 11.884084 12.047918 12.214012 12.382395 12.553099 12.726157 12.901601
## [77,] 12.051317 12.219971 12.390985 12.564392 12.740226 12.918521 13.099311
## [78,] 12.220904 12.394480 12.570522 12.749064 12.930142 13.113792 13.300051
## [79,] 12.392877 12.571482 12.752661 12.936451 13.122890 13.312015 13.503867
## [80,] 12.567270 12.751011 12.937439 13.126592 13.318510 13.513235 13.710806
## [81,] 12.744118 12.933105 13.124894 13.319527 13.517047 13.717496 13.920917
## [82,] 12.923454 13.117798 13.315065 13.515298 13.718543 13.924844 14.134247
## [83,] 13.105313 13.305129 13.507992 13.713947 13.923043 14.135327 14.350847
## [84,] 13.289732 13.495136 13.703714 13.915516 14.130591 14.348991 14.570766
## [85,] 13.476746 13.687855 13.902272 14.120047 14.341233 14.565885 14.794055
## [86,] 13.666392 13.883327 14.103707 14.327584 14.555016 14.786057 15.020766
## [87,] 13.858706 14.081591 14.308060 14.538172 14.771985 15.009558 15.250951
## [88,] 14.053726 14.282685 14.515375 14.751855 14.992188 15.236436 15.484664
## [89,] 14.251491 14.486652 14.725693 14.968679 15.215674 15.466745 15.721958
## [90,] 14.452039 14.693531 14.939059 15.188689 15.442491 15.700534 15.962889
## [91,] 14.655409 14.903365 15.155516 15.411934 15.672690 15.937857 16.207511
## [92,] 14.861641 15.116195 15.375110 15.638459 15.906320 16.178768 16.455883
## [93,] 15.070774 15.332065 15.597885 15.868315 16.143432 16.423320 16.708060
## [94,] 15.282851 15.551017 15.823889 16.101548 16.384080 16.671569 16.964102
## [95,] 15.497912 15.773096 16.053167 16.338210 16.628314 16.923570 17.224068
## [96,] 15.716000 15.998347 16.285767 16.578350 16.876189 17.179380 17.488017
## [97,] 15.937156 16.226814 16.521737 16.822020 17.127760 17.439057 17.756012
## [98,] 16.161425 16.458544 16.761126 17.069271 17.383080 17.702659 18.028113
## [99,] 16.388850 16.693584 17.003984 17.320156 17.642207 17.970246 18.304384
##
## $meta
## $meta$x
## [1] "Pre_Pene_AVG"
##
## $meta$y
## [1] "Density_Num"
##
## $meta$trans
## function (eta)
## pmax(exp(eta), .Machine$double.eps)
## <environment: namespace:stats>
##
## $meta$class
## [1] "negbin" "glm" "lm"
##
## $meta$cond
## Site Year_Fac
## 1 0.5 0.5
##
## $meta$z
## [1] "Post_Burrow_Count"
##
##
## attr(,"class")
## [1] "visreg2d"#By Site
visreg(Burrows_NBglm,
"Pre_Pene_AVG",
scale = "response",
by = "Site",
#breaks = c(0, 4, 8, 12, 16, 20),
ylab = "Crab Burrow Density",
xlab = "Initial Soil Strength"
)
visreg(Post_Pene_lm, "Post_Burrow_Count", by = "Site", overlay = TRUE)
fit <- lm(Ozone ~ Solar.R + Wind + Temp + I(Wind^2) + I(Temp^2) +
I(Wind*Temp)+I(Wind*Temp^2) + I(Temp*Wind^2) + I(Temp^2*Wind^2),
data=airquality)
visreg2d(fit, x="Wind", y="Temp", plot.type="image")
visreg2d(fit, x="Wind", y="Temp", plot.type="image",
color=c("purple", "green", "red"))
visreg2d(fit, x="Wind", y="Temp", plot.type="persp")
## Requires the rgl package
# }
# NOT RUN {
visreg2d(fit,x="Wind",y="Temp",plot.type="rgl")
# }
# NOT RUN {
## Requires the ggplot2 package
# }
# NOT RUN {
visreg2d(fit, x="Wind", y="Temp", plot.type="gg")
#OK, I'll model the same thing for Burrows_NBglm, but for each site
#NAN
Burrows_NBglm_NAN <- glm.nb(data = fidd_NAN,
Post_Burrow_Count ~
Density_Num *
Pre_Pene_AVG +
Year_Fac
,
link = "log"
)
summary(Burrows_NBglm_NAN)##
## Call:
## glm.nb(formula = Post_Burrow_Count ~ Density_Num * Pre_Pene_AVG +
## Year_Fac, data = fidd_NAN, link = "log", init.theta = 8.672265666)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -2.8550 -0.5637 -0.1556 0.5572 1.7420
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 2.7844318 0.2052125 13.569 < 2e-16 ***
## Density_Num 0.0024927 0.0147978 0.168 0.866
## Pre_Pene_AVG 0.0164366 0.0198567 0.828 0.408
## Year_Fac -0.7578080 0.1312603 -5.773 7.77e-09 ***
## Density_Num:Pre_Pene_AVG 0.0005889 0.0015560 0.378 0.705
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for Negative Binomial(8.6723) family taken to be 1)
##
## Null deviance: 96.060 on 47 degrees of freedom
## Residual deviance: 49.324 on 43 degrees of freedom
## AIC: 316.23
##
## Number of Fisher Scoring iterations: 1
##
##
## Theta: 8.67
## Std. Err.: 2.87
##
## 2 x log-likelihood: -304.229#PIE
Burrows_NBglm_PIE <- glm.nb(data = fidd_PIE,
Post_Burrow_Count ~
Density_Num *
Pre_Pene_AVG +
Year_Fac
,
link = "log"
)
summary(Burrows_NBglm_PIE)##
## Call:
## glm.nb(formula = Post_Burrow_Count ~ Density_Num * Pre_Pene_AVG +
## Year_Fac, data = fidd_PIE, link = "log", init.theta = 2.563558483)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -2.4881 -1.0992 -0.0991 0.4727 2.1451
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 1.272735 0.823357 1.546 0.12216
## Density_Num 0.007381 0.070715 0.104 0.91687
## Pre_Pene_AVG -0.031832 0.033008 -0.964 0.33486
## Year_Fac -0.990792 0.319527 -3.101 0.00193 **
## Density_Num:Pre_Pene_AVG 0.002734 0.003196 0.856 0.39224
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for Negative Binomial(2.5636) family taken to be 1)
##
## Null deviance: 76.695 on 47 degrees of freedom
## Residual deviance: 55.167 on 43 degrees of freedom
## AIC: 194.84
##
## Number of Fisher Scoring iterations: 1
##
##
## Theta: 2.56
## Std. Err.: 1.24
##
## 2 x log-likelihood: -182.842summary(Burrows_NBglm)##
## Call:
## glm.nb(formula = Post_Burrow_Count ~ Density_Num * Pre_Pene_AVG +
## Site + Year_Fac, data = combined_data_full, link = "log",
## init.theta = 6.930012647)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -2.6041 -0.9683 -0.1138 0.4572 2.6459
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 0.9879996 0.2690349 3.672 0.00024 ***
## Density_Num -0.0085082 0.0136527 -0.623 0.53316
## Pre_Pene_AVG -0.0131145 0.0125118 -1.048 0.29456
## Site 1.9953157 0.1718184 11.613 < 2e-16 ***
## Year_Fac -0.7975175 0.1220847 -6.532 6.47e-11 ***
## Density_Num:Pre_Pene_AVG 0.0026698 0.0009478 2.817 0.00485 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for Negative Binomial(6.93) family taken to be 1)
##
## Null deviance: 415.55 on 95 degrees of freedom
## Residual deviance: 118.46 on 90 degrees of freedom
## AIC: 506.87
##
## Number of Fisher Scoring iterations: 1
##
##
## Theta: 6.93
## Std. Err.: 2.14
##
## 2 x log-likelihood: -492.875#NAN
# Initial Soil Strength and Crab Density to Final Burrow Density Interaction Heat Map
visreg2d(Burrows_NBglm_NAN,
"Pre_Pene_AVG",
"Density_Num",
scale = "response",
main = "Final Burrow Density NAN",
#by = "Density_Num",
#breaks = c(0, 4, 8, 12, 16, 20),
ylab = "Initial Crab Density",
xlab = "Initial Soil Strength"#,
#plot.type = "rgl"
)
#NAN
visreg(Burrows_NBglm_NAN,
"Density_Num",
scale = "response",
by = c("Pre_Pene_AVG"),
breaks = c(0, 10, 20, 30),
ylab = "Crab Burrow Density",
xlab = "Initial Crab Density",
main = "NAN"
#gg = TRUE
) #+
#theme_bw() #+
#aes(color = "Site")
visreg(Burrows_NBglm_NAN,
"Pre_Pene_AVG",
scale = "response",
by = c("Density_Num"),
breaks = c(0, 4, 8, 12, 16, 20),
ylab = "Crab Burrow Density",
xlab = "Initial Soil Strength",
main = "NAN"
#gg = TRUE
) #+
#theme_bw() #+
#aes(color = "Site")
visreg(Burrows_NBglm_NAN,
"Pre_Pene_AVG",
scale = "response",
#by = c("Density_Num"),
#breaks = c(0, 4, 8, 12, 16, 20),
ylab = "Crab Burrow Density",
xlab = "Initial Soil Strength",
main = "NAN"
#gg = TRUE
) #+## Conditions used in construction of plot
## Density_Num: 10
## Year_Fac: 0.5
#theme_bw() #+
#aes(color = "Site")
#PIE
# Initial Soil Strength and Crab Density to Final Burrow Density Interaction Heat Map
visreg2d(Burrows_NBglm_PIE,
"Pre_Pene_AVG",
"Density_Num",
scale = "response",
main = "Final Burrow Density PIE",
#by = "Density_Num",
#breaks = c(0, 4, 8, 12, 16, 20),
ylab = "Initial Crab Density",
xlab = "Initial Soil Strength"#,
#plot.type = "rgl"
)
#PIE
visreg(Burrows_NBglm_PIE,
"Density_Num",
scale = "response",
by = c("Pre_Pene_AVG"),
breaks = c(0, 10, 20, 30),
ylab = "Crab Burrow Density",
xlab = "Initial Crab Density",
main = "PIE"
#gg = TRUE
) #+
#theme_bw() #+
#aes(color = "Site")
visreg(Burrows_NBglm_PIE,
"Pre_Pene_AVG",
scale = "response",
by = c("Density_Num"),
breaks = c(0, 4, 8, 12, 16, 20),
ylab = "Crab Burrow Density",
xlab = "Initial Soil Strength",
main = "PIE"
#gg = TRUE
) #+
#theme_bw() #+
#aes(color = "Site")
#Compare Initial Soil Strength to Burrow Density
ggplot(data = combined_data_full,
mapping = aes(x = Pre_Pene_AVG,
y = Post_Burrow_Count,
color = Location
)) +
geom_point() +
geom_smooth(method = "lm",
se = FALSE) +
ylab("Number of Burrows per Plot") +
xlab("Initial Soil Strength") +
theme_bw() +
My_Font_Sizes +
Location_Colors_Line
summary(lm(data = combined_data_full, Post_Burrow_Count ~ Pre_Pene_AVG * Location))##
## Call:
## lm(formula = Post_Burrow_Count ~ Pre_Pene_AVG * Location, data = combined_data_full)
##
## Residuals:
## Min 1Q Median 3Q Max
## -15.9840 -3.2044 -0.6768 2.2279 21.6617
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 10.9199 1.4920 7.319 9.15e-11 ***
## Pre_Pene_AVG 0.4909 0.1397 3.515 0.000685 ***
## LocationPIE -9.3655 2.9235 -3.204 0.001866 **
## Pre_Pene_AVG:LocationPIE -0.4460 0.1784 -2.500 0.014204 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 6.39 on 92 degrees of freedom
## Multiple R-squared: 0.5329, Adjusted R-squared: 0.5177
## F-statistic: 34.99 on 3 and 92 DF, p-value: 3.525e-15summary(lm(data = fidd_PIE, Post_Burrow_Count ~ Pre_Pene_AVG))##
## Call:
## lm(formula = Post_Burrow_Count ~ Pre_Pene_AVG, data = fidd_PIE)
##
## Residuals:
## Min 1Q Median 3Q Max
## -3.2155 -2.2538 -0.4523 1.5177 8.2783
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.55435 0.99012 1.570 0.123
## Pre_Pene_AVG 0.04490 0.04373 1.027 0.310
##
## Residual standard error: 2.517 on 46 degrees of freedom
## Multiple R-squared: 0.0224, Adjusted R-squared: 0.001149
## F-statistic: 1.054 on 1 and 46 DF, p-value: 0.3099summary(lm(data = fidd_NAN, Post_Burrow_Count ~ Pre_Pene_AVG))##
## Call:
## lm(formula = Post_Burrow_Count ~ Pre_Pene_AVG, data = fidd_NAN)
##
## Residuals:
## Min 1Q Median 3Q Max
## -15.984 -5.479 -2.928 4.353 21.662
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 10.9199 2.0265 5.389 2.36e-06 ***
## Pre_Pene_AVG 0.4909 0.1897 2.588 0.0129 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 8.68 on 46 degrees of freedom
## Multiple R-squared: 0.1271, Adjusted R-squared: 0.1081
## F-statistic: 6.696 on 1 and 46 DF, p-value: 0.01289#OK, I'll model the same thing for Burrows_NBglm, but for each year
#NAN
Burrows_NBglm_2017 <- glm.nb(data = combined_data_full_2017,
Post_Burrow_Count ~
Density_Num *
Pre_Pene_AVG +
Site
,
link = "log"
)
summary(Burrows_NBglm_2017)##
## Call:
## glm.nb(formula = Post_Burrow_Count ~ Density_Num * Pre_Pene_AVG +
## Site, data = combined_data_full_2017, link = "log", init.theta = 26.73567047)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -2.62162 -1.14612 -0.03518 0.62452 2.35427
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 0.024682 0.301902 0.082 0.935
## Density_Num 0.021463 0.015557 1.380 0.168
## Pre_Pene_AVG -0.012565 0.020513 -0.613 0.540
## Site 1.923375 0.214593 8.963 <2e-16 ***
## Density_Num:Pre_Pene_AVG 0.001686 0.001382 1.220 0.223
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for Negative Binomial(26.7357) family taken to be 1)
##
## Null deviance: 209.887 on 47 degrees of freedom
## Residual deviance: 64.718 on 43 degrees of freedom
## AIC: 217.74
##
## Number of Fisher Scoring iterations: 1
##
##
## Theta: 26.7
## Std. Err.: 36.5
##
## 2 x log-likelihood: -205.741#PIE
Burrows_NBglm_2018 <- glm.nb(data = combined_data_full_2018,
Post_Burrow_Count ~
Density_Num *
Pre_Pene_AVG +
Site
,
link = "log"
)
summary(Burrows_NBglm_2018)##
## Call:
## glm.nb(formula = Post_Burrow_Count ~ Density_Num * Pre_Pene_AVG +
## Site, data = combined_data_full_2018, link = "log", init.theta = 6.294384066)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -2.39566 -0.90104 -0.09547 0.52851 2.56744
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 0.998844 0.381870 2.616 0.00891 **
## Density_Num -0.039365 0.019551 -2.014 0.04406 *
## Pre_Pene_AVG -0.014384 0.015993 -0.899 0.36843
## Site 2.167458 0.251916 8.604 < 2e-16 ***
## Density_Num:Pre_Pene_AVG 0.004024 0.001270 3.169 0.00153 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for Negative Binomial(6.2944) family taken to be 1)
##
## Null deviance: 193.472 on 47 degrees of freedom
## Residual deviance: 57.321 on 43 degrees of freedom
## AIC: 289.19
##
## Number of Fisher Scoring iterations: 1
##
##
## Theta: 6.29
## Std. Err.: 2.27
##
## 2 x log-likelihood: -277.19summary(Burrows_NBglm)##
## Call:
## glm.nb(formula = Post_Burrow_Count ~ Density_Num * Pre_Pene_AVG +
## Site + Year_Fac, data = combined_data_full, link = "log",
## init.theta = 6.930012647)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -2.6041 -0.9683 -0.1138 0.4572 2.6459
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 0.9879996 0.2690349 3.672 0.00024 ***
## Density_Num -0.0085082 0.0136527 -0.623 0.53316
## Pre_Pene_AVG -0.0131145 0.0125118 -1.048 0.29456
## Site 1.9953157 0.1718184 11.613 < 2e-16 ***
## Year_Fac -0.7975175 0.1220847 -6.532 6.47e-11 ***
## Density_Num:Pre_Pene_AVG 0.0026698 0.0009478 2.817 0.00485 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for Negative Binomial(6.93) family taken to be 1)
##
## Null deviance: 415.55 on 95 degrees of freedom
## Residual deviance: 118.46 on 90 degrees of freedom
## AIC: 506.87
##
## Number of Fisher Scoring iterations: 1
##
##
## Theta: 6.93
## Std. Err.: 2.14
##
## 2 x log-likelihood: -492.875#NAN
# Initial Soil Strength and Crab Density to Final Burrow Density Interaction Heat Map
visreg2d(Burrows_NBglm_2017,
"Pre_Pene_AVG",
"Density_Num",
scale = "response",
main = "Final Burrow Density 2017",
#by = "Density_Num",
#breaks = c(0, 4, 8, 12, 16, 20),
ylab = "Initial Crab Density",
xlab = "Initial Soil Strength"#,
#plot.type = "rgl"
)
visreg(Burrows_NBglm_2017,
"Density_Num",
scale = "response",
by = c("Pre_Pene_AVG"),
breaks = c(0, 10, 20, 30),
ylab = "Crab Burrow Density",
xlab = "Initial Crab Density",
main = "2017"
#gg = TRUE
) #+
#theme_bw() #+
#aes(color = "Site")
visreg(Burrows_NBglm_2017,
"Pre_Pene_AVG",
scale = "response",
by = c("Density_Num"),
breaks = c(0, 4, 8, 12, 16, 20),
ylab = "Crab Burrow Density",
xlab = "Initial Soil Strength",
main = "2017"
#gg = TRUE
) #+
#theme_bw() #+
#aes(color = "Site")
visreg2d(Burrows_NBglm_2018,
"Pre_Pene_AVG",
"Density_Num",
scale = "response",
main = "Final Burrow Density 2018",
#by = "Density_Num",
#breaks = c(0, 4, 8, 12, 16, 20),
ylab = "Initial Crab Density",
xlab = "Initial Soil Strength"#,
#plot.type = "rgl"
)
visreg(Burrows_NBglm_2018,
"Density_Num",
scale = "response",
by = c("Pre_Pene_AVG"),
breaks = c(0, 10, 20, 30),
ylab = "Crab Burrow Density",
xlab = "Initial Crab Density",
main = "2018"
#gg = TRUE
) #+
#theme_bw() #+
#aes(color = "Site")
visreg(Burrows_NBglm_2018,
"Pre_Pene_AVG",
scale = "response",
by = c("Density_Num"),
breaks = c(0, 4, 8, 12, 16, 20),
ylab = "Crab Burrow Density",
xlab = "Initial Soil Strength",
main = "2018"
#gg = TRUE
) #+
#theme_bw() #+
#aes(color = "Site")
visreg(Burrows_NBglm,
"Site",
scale = "response",
by = c("Year_Fac"),
#breaks = c(0, 4, 8, 12, 16, 20),
ylab = "Crab Burrow Density",
xlab = "Site"#,
#main = "2018"
#gg = TRUE
) #+
#theme_bw() #+
#aes(color = "Site")
#OK, now let's look at the combined affect of burrows and initial soil strength on final soil strength
visreg2d(Post_Pene_lm,
"Pre_Pene_AVG",
"Post_Burrow_Count",
scale = "response",
main = "Final Soil Strength",
#by = "Density_Num",
#breaks = c(0, 4, 8, 12, 16, 20),
ylab = "Final Burrow Count",
xlab = "Initial Soil Strength"#,
#plot.type = "rgl"
)
PSEM Combined Ecosystem Models
EF Model Combinations
- Soil Strength and Primary Production
- Soil Strength, Primary Production, and Decomposition
- Soil Strength, Primary Production, and Belowground Biomass (Belowground Production)
- Soil Strength, Primary Production, Decomposition, and Belowground Biomass (Belowground Production)
There are the models generated by the psem package, also I created SEM models using DiagrammeR. Below is a key for understanding what each model type components mean:
SEM Visualization Key
Squares = Nodes (variables/parameters)
Arrows = The direction that on variable influences the other
Solid Line = A Significant Interaction (p<0.5)
Dashed Line = A Non-Significant Interaction (p>0.5)
DiagrammeR Visualization Key
(Created because the PSEM plot got complicated, and this cleaned things up)
Circle = Fully Exogenous (Predictor) Node (Variable)
Square = Endogenous (Response) Node, but can also be exogenous to another node. Exhibits some endogeneity tho
Solid Thick Red Line = Significant Relationship (p<0.5)
Solid Thin Black Line = Non-Significant Relationship (p>0.5)
Most of the Non-Significant relationships have been removed for clarity, with only a few added for explanatory purposes
Model Output
Soil and Production Models
# Piecewise (Local) SEM
## Soil Strength
Post_Pene_combined_lm <- lm(data = combined_data_full,
Post_Pene_AVG ~
Post_Burrow_Count +
Pre_Pene_AVG +
Site +
Year_Fac +
Pre_Live_SD *
Post_Live_SD
)
summary(Post_Pene_combined_lm)##
## Call:
## lm(formula = Post_Pene_AVG ~ Post_Burrow_Count + Pre_Pene_AVG +
## Site + Year_Fac + Pre_Live_SD * Post_Live_SD, data = combined_data_full)
##
## Residuals:
## Min 1Q Median 3Q Max
## -19.1268 -4.8787 0.7837 3.7896 19.8422
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 16.884316 5.620289 3.004 0.00347 **
## Post_Burrow_Count -0.351139 0.141193 -2.487 0.01477 *
## Pre_Pene_AVG 0.303900 0.114685 2.650 0.00955 **
## Site -9.932397 3.013373 -3.296 0.00141 **
## Year_Fac -0.428558 3.251343 -0.132 0.89544
## Pre_Live_SD 0.326845 0.103168 3.168 0.00211 **
## Post_Live_SD 0.192966 0.124800 1.546 0.12564
## Pre_Live_SD:Post_Live_SD -0.006196 0.002449 -2.530 0.01320 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 7.713 on 88 degrees of freedom
## Multiple R-squared: 0.6114, Adjusted R-squared: 0.5805
## F-statistic: 19.78 on 7 and 88 DF, p-value: 1.121e-15summary(lm(data = combined_data_full, Post_Pene_AVG ~ Year * Site))##
## Call:
## lm(formula = Post_Pene_AVG ~ Year * Site, data = combined_data_full)
##
## Residuals:
## Min 1Q Median 3Q Max
## -24.0971 -4.0442 0.2136 4.4662 23.9029
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 25.806 1.652 15.619 < 2e-16 ***
## Year2018 8.791 2.336 3.763 0.000296 ***
## Site -10.792 2.336 -4.619 1.25e-05 ***
## Year2018:Site -11.195 3.304 -3.388 0.001037 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 8.094 on 92 degrees of freedom
## Multiple R-squared: 0.5526, Adjusted R-squared: 0.538
## F-statistic: 37.87 on 3 and 92 DF, p-value: 4.955e-16#Burrows
Burrows_combined_NBglm <- glm.nb(data = combined_data_full,
Post_Burrow_Count ~
Density_Num *
Pre_Pene_AVG +
Year_Fac +
Site
,
link = "log"
)
summary(Burrows_combined_NBglm)##
## Call:
## glm.nb(formula = Post_Burrow_Count ~ Density_Num * Pre_Pene_AVG +
## Year_Fac + Site, data = combined_data_full, link = "log",
## init.theta = 6.930012647)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -2.6041 -0.9683 -0.1138 0.4572 2.6459
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 0.9879996 0.2690349 3.672 0.00024 ***
## Density_Num -0.0085082 0.0136527 -0.623 0.53316
## Pre_Pene_AVG -0.0131145 0.0125118 -1.048 0.29456
## Year_Fac -0.7975175 0.1220847 -6.532 6.47e-11 ***
## Site 1.9953157 0.1718184 11.613 < 2e-16 ***
## Density_Num:Pre_Pene_AVG 0.0026698 0.0009478 2.817 0.00485 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for Negative Binomial(6.93) family taken to be 1)
##
## Null deviance: 415.55 on 95 degrees of freedom
## Residual deviance: 118.46 on 90 degrees of freedom
## AIC: 506.87
##
## Number of Fisher Scoring iterations: 1
##
##
## Theta: 6.93
## Std. Err.: 2.14
##
## 2 x log-likelihood: -492.875#Initial Soil Strength
Pre_Pene_combined_lm <- lm(data = combined_data_full,
Pre_Pene_AVG ~
Site +
Year_Fac
)
summary(Pre_Pene_combined_lm)##
## Call:
## lm(formula = Pre_Pene_AVG ~ Site + Year_Fac, data = combined_data_full)
##
## Residuals:
## Min 1Q Median 3Q Max
## -15.3959 -4.8117 -0.7326 4.7732 18.6041
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 23.729 1.260 18.838 < 2e-16 ***
## Site -12.667 1.455 -8.709 1.1e-13 ***
## Year_Fac -5.334 1.455 -3.667 0.000409 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 7.126 on 93 degrees of freedom
## Multiple R-squared: 0.4898, Adjusted R-squared: 0.4788
## F-statistic: 44.64 on 2 and 93 DF, p-value: 2.566e-14#Spartina Biomass
SB_Gamma_combined_glm <- glm(data = combined_data_full,
Spartina_Biomass ~
Pre_Live_SD *
Post_Live_SD +
Post_Burrow_Count *
Pre_Pene_AVG +
Density_Num +
#Post_Live_SD *
#Post_Pene_AVG +
Site +
Year_Fac,
family = Gamma(link = "log")
)
summary(SB_Gamma_combined_glm)##
## Call:
## glm(formula = Spartina_Biomass ~ Pre_Live_SD * Post_Live_SD +
## Post_Burrow_Count * Pre_Pene_AVG + Density_Num + Site + Year_Fac,
## family = Gamma(link = "log"), data = combined_data_full)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -4.8399 -0.4345 -0.0719 0.2900 1.1544
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 3.8956670 0.4449234 8.756 1.55e-13 ***
## Pre_Live_SD 0.0228097 0.0074587 3.058 0.002969 **
## Post_Live_SD 0.0360421 0.0090869 3.966 0.000151 ***
## Post_Burrow_Count 0.0047408 0.0155563 0.305 0.761290
## Pre_Pene_AVG -0.0318516 0.0107996 -2.949 0.004101 **
## Density_Num 0.0070573 0.0086570 0.815 0.417200
## Site -1.2738128 0.2203284 -5.781 1.17e-07 ***
## Year_Fac -0.2153392 0.2340160 -0.920 0.360047
## Pre_Live_SD:Post_Live_SD -0.0006491 0.0001791 -3.625 0.000489 ***
## Post_Burrow_Count:Pre_Pene_AVG 0.0001576 0.0009450 0.167 0.867961
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for Gamma family taken to be 0.3069862)
##
## Null deviance: 115.261 on 95 degrees of freedom
## Residual deviance: 89.142 on 86 degrees of freedom
## AIC: 942.56
##
## Number of Fisher Scoring iterations: 11#Final Shoot Density (SD)
SD_combined_NBglm <- glm.nb(data = combined_data_full,
Post_Live_SD ~
Density_Num +
Post_Burrow_Count +
Pre_Live_SD +
Pre_Pene_AVG +
Site +
Year_Fac,
link = "log"
)
summary(SD_combined_NBglm)##
## Call:
## glm.nb(formula = Post_Live_SD ~ Density_Num + Post_Burrow_Count +
## Pre_Live_SD + Pre_Pene_AVG + Site + Year_Fac, data = combined_data_full,
## link = "log", init.theta = 8.491743906)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -3.6202 -0.6651 -0.1680 0.5167 3.1613
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 3.372364 0.229853 14.672 < 2e-16 ***
## Density_Num -0.002779 0.006163 -0.451 0.652
## Post_Burrow_Count -0.000808 0.007183 -0.112 0.910
## Pre_Live_SD 0.013083 0.003287 3.981 6.87e-05 ***
## Pre_Pene_AVG -0.008070 0.006070 -1.330 0.184
## Site -0.138288 0.161797 -0.855 0.393
## Year_Fac -0.898886 0.140735 -6.387 1.69e-10 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for Negative Binomial(8.4917) family taken to be 1)
##
## Null deviance: 324.03 on 95 degrees of freedom
## Residual deviance: 108.45 on 89 degrees of freedom
## AIC: 715.96
##
## Number of Fisher Scoring iterations: 1
##
##
## Theta: 8.49
## Std. Err.: 1.79
##
## 2 x log-likelihood: -699.961SD_nb_res_combined <- simulateResiduals(Burrows_combined_NBglm)
plot(SD_nb_res_combined)
#Running the combined model
combined_SEM <- psem(Post_Pene_combined_lm,
Burrows_combined_NBglm,
SB_Gamma_combined_glm,
SD_combined_NBglm,
Pre_Pene_combined_lm)
summary(combined_SEM)##
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## Structural Equation Model of combined_SEM
##
## Call:
## Post_Pene_AVG ~ Post_Burrow_Count + Pre_Pene_AVG + Site + Year_Fac + Pre_Live_SD * Post_Live_SD
## Post_Burrow_Count ~ Density_Num * Pre_Pene_AVG + Year_Fac + Site
## Spartina_Biomass ~ Pre_Live_SD * Post_Live_SD + Post_Burrow_Count * Pre_Pene_AVG + Density_Num + Site + Year_Fac
## Post_Live_SD ~ Density_Num + Post_Burrow_Count + Pre_Live_SD + Pre_Pene_AVG + Site + Year_Fac
## Pre_Pene_AVG ~ Site + Year_Fac
##
## AIC BIC
## 91.032 191.042
##
## ---
## Tests of directed separation:
##
## Independ.Claim Test.Type DF Crit.Value P.Value
## Pre_Pene_AVG ~ Pre_Live_SD + ... coef 92 -1.0718 0.2866
## Post_Burrow_Count ~ Pre_Live_SD + ... coef 89 -1.6348 0.1021
## Pre_Pene_AVG ~ Density_Num + ... coef 92 -0.7572 0.4508
## Post_Pene_AVG ~ Density_Num + ... coef 87 -0.4998 0.6185
## Spartina_Biomass ~ Post_Pene_AVG + ... coef 85 -1.3477 0.1813
##
## Global goodness-of-fit:
##
## Fisher's C = 13.032 with P-value = 0.222 and on 10 degrees of freedom
##
## ---
## Coefficients:
##
## Response Predictor Estimate Std.Error DF
## Post_Pene_AVG Post_Burrow_Count -0.3511 0.1412 88
## Post_Pene_AVG Pre_Pene_AVG 0.3039 0.1147 88
## Post_Pene_AVG Site -9.9324 3.0134 88
## Post_Pene_AVG Year_Fac -0.4286 3.2513 88
## Post_Pene_AVG Pre_Live_SD 0.3268 0.1032 88
## Post_Pene_AVG Post_Live_SD 0.1930 0.1248 88
## Post_Pene_AVG Pre_Live_SD:Post_Live_SD -0.0062 0.0024 88
## Post_Burrow_Count Density_Num -0.0085 0.0137 90
## Post_Burrow_Count Pre_Pene_AVG -0.0131 0.0125 90
## Post_Burrow_Count Year_Fac -0.7975 0.1221 90
## Post_Burrow_Count Site 1.9953 0.1718 90
## Post_Burrow_Count Density_Num:Pre_Pene_AVG 0.0027 0.0009 90
## Spartina_Biomass Pre_Live_SD 0.0228 0.0075 86
## Spartina_Biomass Post_Live_SD 0.0360 0.0091 86
## Spartina_Biomass Post_Burrow_Count 0.0047 0.0156 86
## Spartina_Biomass Pre_Pene_AVG -0.0319 0.0108 86
## Spartina_Biomass Density_Num 0.0071 0.0087 86
## Spartina_Biomass Site -1.2738 0.2203 86
## Spartina_Biomass Year_Fac -0.2153 0.2340 86
## Spartina_Biomass Pre_Live_SD:Post_Live_SD -0.0006 0.0002 86
## Spartina_Biomass Post_Burrow_Count:Pre_Pene_AVG 0.0002 0.0009 86
## Post_Live_SD Density_Num -0.0028 0.0062 89
## Post_Live_SD Post_Burrow_Count -0.0008 0.0072 89
## Post_Live_SD Pre_Live_SD 0.0131 0.0033 89
## Post_Live_SD Pre_Pene_AVG -0.0081 0.0061 89
## Post_Live_SD Site -0.1383 0.1618 89
## Post_Live_SD Year_Fac -0.8989 0.1407 89
## Pre_Pene_AVG Site -12.6669 1.4545 93
## Pre_Pene_AVG Year_Fac -5.3335 1.4545 93
## Crit.Value P.Value Std.Estimate
## -2.4869 0.0148 -0.2713 *
## 2.6499 0.0095 0.2519 **
## -3.2961 0.0014 -0.4192 **
## -0.1318 0.8954 -0.0181
## 3.1681 0.0021 0.5226 **
## 1.5462 0.1256 0.3041
## -2.5296 0.0132 -0.6179 *
## -0.6232 0.5332 -
## -1.0482 0.2946 -
## -6.5325 0.0000 - ***
## 11.6129 0.0000 - ***
## 2.8167 0.0049 - **
## 3.0581 0.0030 - **
## 3.9664 0.0002 - ***
## 0.3048 0.7613 -
## -2.9493 0.0041 - **
## 0.8152 0.4172 -
## -5.7814 0.0000 - ***
## -0.9202 0.3600 -
## -3.6248 0.0005 - ***
## 0.1667 0.8680 -
## -0.4509 0.6520 -
## -0.1125 0.9104 -
## 3.9808 0.0001 - ***
## -1.3296 0.1837 -
## -0.8547 0.3927 -
## -6.3871 0.0000 - ***
## -8.7087 0.0000 -0.645 ***
## -3.6669 0.0004 -0.2716 ***
##
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05
##
## ---
## Individual R-squared:
##
## Response method R.squared
## Post_Pene_AVG none 0.61
## Post_Burrow_Count nagelkerke 0.97
## Spartina_Biomass nagelkerke 0.34
## Post_Live_SD nagelkerke 0.93
## Pre_Pene_AVG none 0.49 #plot(combined_SEM, show = "Estimate")Soil and Production DAGs
# DiagrammeR Plots
## Including Site and Year
grViz("digraph Soil_Strength {
# a 'graph' statement
graph [overlap = false,
fontsize = 14]
# several 'node' statements
# Exogenous Variables
node [shape = rectangle,
fontname = Helvetica,
width = 1.3,
fontcolor = darkslategray,
color = darkslategray,
nodesep = 1,
penwidth = 2]
Crab_Density [label = '@@1']
Site [label = '@@5']
Year [label = '@@6']
# Endogenous Variables
node [shape = rectangle,
fixedsize = true,
width = 1.8,
color = steelblue,
fontcolor = darkslategray,
penwidth = 2]
Burrow_Density [label = '@@3']
Initial_SS [label = '@@4', color = darkslategray]
Final_SS [label = '@@7']
# Soil Strength Interaction
node [shape = rectangle,
fixedsize = true,
width = 2,
height = 0.9,
color = steelblue,
fontcolor = darkslategray,
penwidth = 2]
CrabSoil_Intrctn [label = '@@2']
# Primary Production
node [shape = rectangle,
fixedsize = true,
width = 2,
color = forestgreen,
fontcolor = darkslategray,
penwidth = 2]
Pre_Live_SD [label = '@@8']
Spartina_Biomass [label = '@@9']
Post_Live_SD [label = '@@10']
Pre_post_Intrctn [label = '@@11', height = 0.9]
# Soil Shoots Interaction
node [shape = rectangle,
fixedsize = true,
width = 2.2,
height = 0.9,
color = CadetBlue,
fontcolor = darkslategray,
penwidth = 2]
SoilShoots_Intrctn [label = '@@12']
# several 'edge' statements
#Soil Strength Exogenous Variables
edge [color = grey, arrowhead = normal, penwidth = 1, minlen = 3]
Initial_SS->Burrow_Density
Crab_Density->Burrow_Density
Initial_SS->Spartina_Biomass [color = forestgreen, arrowhead = normal, penwidth = 5, minlen = 3]
Initial_SS->Post_Live_SD
#Primary Production Exogenous Variables
edge [color = forestgreen, arrowhead = normal, penwidth = 5, minlen = 3]
Pre_Live_SD -> Final_SS
Pre_Live_SD -> Spartina_Biomass
Pre_Live_SD -> Post_Live_SD
Pre_post_Intrctn -> Spartina_Biomass
Pre_post_Intrctn -> Final_SS
Burrow_Density -> Spartina_Biomass [color = grey, arrowhead = normal, penwidth = 1, minlen = 3]
Final_SS -> Spartina_Biomass [color = grey, arrowhead = normal, penwidth = 1, minlen = 3]
Burrow_Density -> Post_Live_SD [color = grey, arrowhead = normal, penwidth = 1, minlen = 3]
#All Endogenous Variables
edge [color = DimGray, arrowhead = normal, penwidth = 5, minlen = 5]
Site->Burrow_Density
Year->Burrow_Density
Burrow_Density->Final_SS [color = steelblue]
Site->Initial_SS
Year->Initial_SS
Site->Final_SS
Year->Final_SS
Initial_SS->Final_SS
Year -> Post_Live_SD
Post_Live_SD->Spartina_Biomass [color = forestgreen]
Site -> Spartina_Biomass
edge [color = steelblue, arrowhead = normal, penwidth = 5, minlen = 4]
CrabSoil_Intrctn->Burrow_Density
edge [color = CadetBlue arrowhead = normal, penwidth = 5, minlen = 4]
SoilShoots_Intrctn->Spartina_Biomass
}
[1]: 'Crab Density'
[2]: 'Crab Density and\\nInitial Soil Strength\\nInteraction\\n'
[3]: 'Burrow Density'
[4]: 'Initial Soil Strength'
[5]: 'Site'
[6]: 'Year'
[7]: 'Final Soil Strength'
[8]: 'Initial Shoot Density'
[9]: 'Spartina Biomass'
[10]: 'Final Shoot Density'
[11]: 'Initial Shoot Density and\\nFinal Shoot Density\\nInteraction\\n'
[12]: 'Final Soil Strength and\\nFinal Shoot Density\\nInteraction\\n'
"
) ## Omitting Site and Year
grViz("digraph Soil_Strength {
# a 'graph' statement
graph [overlap = false,
fontsize = 14]
# several 'node' statements
# Exogenous Variables
node [shape = rectangle,
fontname = Helvetica,
width = 1.3,
fontcolor = darkslategray,
color = darkslategray,
nodesep = 1,
penwidth = 2]
Crab_Density [label = '@@1']
# Endogenous Variables
node [shape = rectangle,
fixedsize = true,
width = 1.8,
color = steelblue,
fontcolor = darkslategray,
penwidth = 2]
Burrow_Density [label = '@@3']
Initial_SS [label = '@@4', color = darkslategray]
Final_SS [label = '@@5']
# Soil Strength Interaction
node [shape = rectangle,
fixedsize = true,
width = 2,
height = 0.9,
color = steelblue,
fontcolor = darkslategray,
penwidth = 2]
CrabSoil_Intrctn [label = '@@2']
# Primary Production
node [shape = rectangle,
fixedsize = true,
width = 2,
color = forestgreen,
fontcolor = darkslategray,
penwidth = 2]
Pre_Live_SD [label = '@@6']
Spartina_Biomass [label = '@@7']
Post_Live_SD [label = '@@8']
Pre_post_Intrctn [label = '@@9', height = 0.9, width = 2.2]
# Soil Shoots Interaction
node [shape = rectangle,
fixedsize = true,
width = 2.1,
height = 0.9,
color = CadetBlue,
fontcolor = darkslategray,
penwidth = 2]
SoilShoots_Intrctn [label = '@@10']
# several 'edge' statements
#Soil Strength Exogenous Variables
edge [color = grey, arrowhead = normal, penwidth = 1, minlen = 3]
Initial_SS->Burrow_Density
Crab_Density->Burrow_Density
Initial_SS->Spartina_Biomass [color = forestgreen, arrowhead = normal, penwidth = 5, minlen = 3]
Initial_SS->Post_Live_SD
#Primary Production Exogenous Variables
edge [color = forestgreen, arrowhead = normal, penwidth = 5, minlen = 3]
Pre_Live_SD -> Final_SS
Pre_Live_SD -> Spartina_Biomass
Pre_Live_SD -> Post_Live_SD
Pre_post_Intrctn -> Spartina_Biomass
Pre_post_Intrctn -> Final_SS
Burrow_Density -> Spartina_Biomass [color = grey, arrowhead = normal, penwidth = 1, minlen = 3]
Final_SS -> Spartina_Biomass [color = grey, arrowhead = normal, penwidth = 1, minlen = 3]
Burrow_Density -> Post_Live_SD [color = grey, arrowhead = normal, penwidth = 1, minlen = 3]
#All Endogenous Variables
edge [color = DimGray, arrowhead = normal, penwidth = 5, minlen = 5]
Burrow_Density->Final_SS [color = steelblue]
Initial_SS->Final_SS
Post_Live_SD->Spartina_Biomass [color = forestgreen]
Post_Live_SD->Final_SS [color = grey, arrowhead = normal, penwidth = 1, minlen = 3]
Crab_Density->Spartina_Biomass [color = grey, arrowhead = normal, penwidth = 1, minlen = 3]
#Crab Density and Soil Strength Interaction
edge [color = steelblue, arrowhead = normal, penwidth = 5, minlen = 4]
CrabSoil_Intrctn->Burrow_Density
#Soil Strength and Final Shoot Density Interaction
edge [color = CadetBlue arrowhead = normal, penwidth = 5, minlen = 4]
SoilShoots_Intrctn->Spartina_Biomass
}
[1]: 'Crab Density'
[2]: 'Crab Density and\\nInitial Soil Strength\\nInteraction\\n'
[3]: 'Burrow Density'
[4]: 'Initial Soil Strength'
[5]: 'Final Soil Strength'
[6]: 'Initial Shoot Density'
[7]: 'Spartina Biomass'
[8]: 'Final Shoot Density'
[9]: 'Initial Shoot Density and\\nFinal Shoot Density\\nInteraction\\n'
[10]: 'Final Soil Strength and\\nFinal Shoot Density\\nInteraction\\n'
"
) #grViz("
#digraph test {
# graph [fontsize = 10]
# node [shape = box]
# A [label = 'Foo\\lBar\\l']
# B [label = 'Bar\\rFoo\\r']
# A -> B
# }
#")
#plot(combined_SEM, show = "unstd")
#coefs(combined_SEM, intercepts = TRUE)
#rsquared(combined_SEM)Soil and Production Visreg
visreg2d(Post_Pene_combined_lm,
"Pre_Live_SD",
"Post_Live_SD",
scale = "response",
main = "Final Soil Strength",
#by = "Density_Num",
#breaks = c(0, 4, 8, 12, 16, 20),
ylab = "Initial S. alterniflora Density",
xlab = "Final S. alterniflora Density"#,
#plot.type = "rgl"
)
visreg2d(SB_Gamma_combined_glm,
"Pre_Live_SD",
"Post_Live_SD",
scale = "response",
main = "Spartina alterniflora Biomass",
#by = "Density_Num",
#breaks = c(0, 4, 8, 12, 16, 20),
ylab = "Initial S. alterniflora Density",
xlab = "Final S. alterniflora Density"#,
#plot.type = "rgl"
)
visreg(Post_Pene_combined_lm,
"Post_Live_SD",
by = "Site",
scale = "response")
#Get the SE
SD_Site_SE <- summarySE(combined_data_full, measurevar = "Post_Live_SD",
groupvars = c("Location"))
#Plot it!
ggplot(data = SD_Site_SE, aes(x = Location,
y = Post_Live_SD,
fill = Location)) +
geom_bar(position = position_dodge(), stat = "identity",
width = 0.50) +
expand_limits(y = c(0, 1)) +
geom_errorbar(aes(ymin = Post_Live_SD - se, ymax = Post_Live_SD + se),
width = .1, # Width of the error bars
position=position_dodge(.9)) +
ylab("Final Shoot Density") +
xlab("Location") +
theme_bw() +
My_Font_Sizes +
Location_Colors_Bar
#Get the SE
SB_Site_SE <- summarySE(combined_data_full, measurevar = "Spartina_Biomass",
groupvars = c("Location"))
#Plot it!
ggplot(data = SB_Site_SE, aes(x = Location,
y = Spartina_Biomass,
fill = Location)) +
geom_bar(position = position_dodge(), stat = "identity",
width = 0.50) +
expand_limits(y = c(0, 1)) +
geom_errorbar(aes(ymin = Spartina_Biomass - se, ymax = Spartina_Biomass + se),
width = .1, # Width of the error bars
position=position_dodge(.9)) +
ylab("Spartina Biomass") +
xlab("Location") +
theme_bw() +
My_Font_Sizes +
Location_Colors_Bar
summary(lm(Post_Live_SD ~ Location, data = combined_data_full))##
## Call:
## lm(formula = Post_Live_SD ~ Location, data = combined_data_full)
##
## Residuals:
## Min 1Q Median 3Q Max
## -28.437 -14.635 -6.437 13.771 60.562
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 28.437 2.718 10.463 <2e-16 ***
## LocationPIE -2.208 3.844 -0.575 0.567
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 18.83 on 94 degrees of freedom
## Multiple R-squared: 0.003499, Adjusted R-squared: -0.007102
## F-statistic: 0.3301 on 1 and 94 DF, p-value: 0.567summary(lm(Pre_Live_SD ~ Location, data = combined_data_full))##
## Call:
## lm(formula = Pre_Live_SD ~ Location, data = combined_data_full)
##
## Residuals:
## Min 1Q Median 3Q Max
## -38.625 -13.047 -1.125 12.146 50.375
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 38.625 2.626 14.71 < 2e-16 ***
## LocationPIE -11.771 3.713 -3.17 0.00206 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 18.19 on 94 degrees of freedom
## Multiple R-squared: 0.09657, Adjusted R-squared: 0.08696
## F-statistic: 10.05 on 1 and 94 DF, p-value: 0.002059summary(lm(Spartina_Biomass ~ Location, data = combined_data_full))##
## Call:
## lm(formula = Spartina_Biomass ~ Location, data = combined_data_full)
##
## Residuals:
## Min 1Q Median 3Q Max
## -61.063 -22.663 -3.622 13.413 144.257
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 34.757 4.994 6.960 4.54e-10 ***
## LocationPIE 33.066 7.063 4.682 9.54e-06 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 34.6 on 94 degrees of freedom
## Multiple R-squared: 0.1891, Adjusted R-squared: 0.1805
## F-statistic: 21.92 on 1 and 94 DF, p-value: 9.542e-06#Get the SE
Pre_SD_Site_SE <- summarySE(combined_data_full, measurevar = "Pre_Live_SD",
groupvars = c("Location"))
#Plot it!
ggplot(data = Pre_SD_Site_SE, aes(x = Location,
y = Pre_Live_SD,
fill = Location)) +
geom_bar(position = position_dodge(), stat = "identity",
width = 0.50) +
expand_limits(y = c(0, 1)) +
geom_errorbar(aes(ymin = Pre_Live_SD - se, ymax = Pre_Live_SD + se),
width = .1, # Width of the error bars
position=position_dodge(.9)) +
ylab("Initial Shoot Density") +
xlab("Location") +
theme_bw() +
My_Font_Sizes +
Location_Colors_Bar
ggplot(data = combined_data_full, aes(x = Pre_Live_SD,
y = Post_Live_SD,
color = Location)) +
geom_point() +
geom_smooth(method = "lm") +
ylab("Final Shoot Density") +
xlab("Initial Shoot Density") +
theme_bw() +
My_Font_Sizes +
Location_Colors_Line
summary(lm(Post_Live_SD ~ Pre_Live_SD + Location, data = combined_data_full))##
## Call:
## lm(formula = Post_Live_SD ~ Pre_Live_SD + Location, data = combined_data_full)
##
## Residuals:
## Min 1Q Median 3Q Max
## -29.337 -7.978 -3.026 5.906 51.416
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -0.11164 3.47616 -0.032 0.9744
## Pre_Live_SD 0.73914 0.07514 9.836 4.54e-16 ***
## LocationPIE 6.49192 2.84627 2.281 0.0248 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 13.25 on 93 degrees of freedom
## Multiple R-squared: 0.5116, Adjusted R-squared: 0.5011
## F-statistic: 48.71 on 2 and 93 DF, p-value: 3.374e-15#Get the SE
SS_Site_SE <- summarySE(combined_data_full, measurevar = "Post_Pene_AVG",
groupvars = c("Location"))
#Plot it!
ggplot(data = SS_Site_SE, aes(x = Location,
y = Post_Pene_AVG,
fill = Location)) +
geom_bar(position = position_dodge(), stat = "identity",
width = 0.50) +
expand_limits(y = c(0, 1)) +
geom_errorbar(aes(ymin = Post_Pene_AVG - se, ymax = Post_Pene_AVG + se),
width = .1, # Width of the error bars
position=position_dodge(.9)) +
ylab("Final Soil Strength") +
xlab("Location") +
theme_bw() +
My_Font_Sizes +
Location_Colors_Bar
#Get the SE
SS_Initial_Site_SE <- summarySE(combined_data_full, measurevar = "Pre_Pene_AVG",
groupvars = c("Location"))
#Plot it!
ggplot(data = SS_Initial_Site_SE, aes(x = Location,
y = Pre_Pene_AVG,
fill = Location)) +
geom_bar(position = position_dodge(), stat = "identity",
width = 0.50) +
expand_limits(y = c(0, 1)) +
geom_errorbar(aes(ymin = Pre_Pene_AVG - se, ymax = Pre_Pene_AVG + se),
width = .1, # Width of the error bars
position=position_dodge(.9)) +
ylab("Initial Soil Strength") +
xlab("Location") +
theme_bw() +
My_Font_Sizes +
Location_Colors_Bar
Burrows_Site_SE <- summarySE(combined_data_full, measurevar = "Post_Burrow_Count",
groupvars = c("Density_NN"))
#Plot it!
ggplot(data = Burrows_Site_SE, aes(x = Density_NN,
y = Post_Burrow_Count,
fill = Density_NN)) +
geom_bar(position = position_dodge(), stat = "identity",
width = 0.50) +
expand_limits(y = c(0, 1)) +
geom_errorbar(aes(ymin = Post_Burrow_Count - se, ymax = Post_Burrow_Count + se),
width = .1, # Width of the error bars
position=position_dodge(.9)) +
ylab("Burrow Density") +
xlab("Initial Crab Density") +
theme_bw() +
My_Font_Sizes
#Compare Initial Soil Strength to Burrow Density
ggplot(data = combined_data_full,
mapping = aes(x = Pre_Pene_AVG,
y = Post_Burrow_Count,
color = Location
)) +
geom_point() +
geom_smooth(method = "lm",
se = FALSE) +
ylab("Number of Burrows per Plot") +
xlab("Initial Soil Strength") +
theme_bw() +
My_Font_Sizes +
Location_Colors_Line
ggplot(data = combined_data_full,
mapping = aes(x = Post_Burrow_Count,
y = Post_Pene_AVG,
color = Location
)) +
geom_point() +
geom_smooth(method = "lm",
#se = FALSE
) +
xlab("Number of Burrows per Plot") +
ylab("Final Soil Strength") +
theme_bw() +
My_Font_Sizes +
Location_Colors_Line
summary(lm(Post_Pene_AVG ~ Post_Burrow_Count + Location, data = combined_data_full))##
## Call:
## lm(formula = Post_Pene_AVG ~ Post_Burrow_Count + Location, data = combined_data_full)
##
## Residuals:
## Min 1Q Median 3Q Max
## -20.1078 -5.3896 0.7218 4.2736 28.3799
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 16.2568 2.3426 6.940 5.18e-10 ***
## Post_Burrow_Count -0.1625 0.1320 -1.232 0.221
## LocationPIE 14.3510 2.4156 5.941 4.88e-08 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 8.62 on 93 degrees of freedom
## Multiple R-squared: 0.487, Adjusted R-squared: 0.4759
## F-statistic: 44.14 on 2 and 93 DF, p-value: 3.328e-14ggplot(data = combined_data_full,
mapping = aes(y = Post_Burrow_Count,
x = Post_Pene_AVG,
color = Location
)) +
geom_point() +
geom_smooth(method = "lm",
se = FALSE) +
ylab("Number of Burrows per Plot") +
xlab("Final Soil Strength") +
theme_bw() +
My_Font_Sizes +
Location_Colors_Line
#Compare Initial Soil Strength to Burrow Density
ggplot(data = combined_data_full,
mapping = aes(x = Pre_Pene_AVG,
y = Post_Burrow_Count,
color = Density_NN,
shape = Location
)) +
geom_point() +
geom_smooth(method = "lm",
se = FALSE) +
ylab("Number of Burrows per Plot") +
xlab("Initial Soil Strength") +
theme_bw() +
My_Font_Sizes #+
#Location_Colors_Line
#Compare Initial Crab Density to Burrow Density
ggplot(data = combined_data_full,
mapping = aes(x = Density_Num,
y = Post_Burrow_Count,
color = Location
)) +
geom_point() +
geom_smooth(method = "loess") +
scale_x_continuous(breaks = c(0, 4, 8, 12, 16, 20)) +
ylab("Number of Burrows per Plot") +
xlab("Initial Crab Density") +
theme_bw() +
My_Font_Sizes +
Location_Colors_Line
Decomposition Models
#Building the Models
#Soil Strength
Post_Pene_combined_lm_2 <- lm(data = Decomp_2018_3,
Post_Pene_AVG ~
Site +
Post_Burrow_Count +
Pre_Pene_AVG +
Pre_Live_SD *
Post_Live_SD
)
summary(Post_Pene_combined_lm_2)##
## Call:
## lm(formula = Post_Pene_AVG ~ Site + Post_Burrow_Count + Pre_Pene_AVG +
## Pre_Live_SD * Post_Live_SD, data = Decomp_2018_3)
##
## Residuals:
## Min 1Q Median 3Q Max
## -16.3079 -4.6554 0.1846 4.5451 19.1761
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 8.74109 8.41545 1.039 0.302155
## Site -15.18180 3.85698 -3.936 0.000179 ***
## Post_Burrow_Count -0.15021 0.13849 -1.085 0.281450
## Pre_Pene_AVG 0.28715 0.13911 2.064 0.042328 *
## Pre_Live_SD 0.51163 0.15848 3.228 0.001822 **
## Post_Live_SD 0.37507 0.17310 2.167 0.033304 *
## Pre_Live_SD:Post_Live_SD -0.01002 0.00357 -2.806 0.006331 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 8.181 on 78 degrees of freedom
## Multiple R-squared: 0.6856, Adjusted R-squared: 0.6614
## F-statistic: 28.34 on 6 and 78 DF, p-value: < 2.2e-16#Wider Data
Post_Pene_combined_lm_Wider <- lm(data = Decomp_2018_Wider_2,
Post_Pene_AVG ~
Site +
Post_Burrow_Count +
Pre_Pene_AVG +
Pre_Live_SD *
Post_Live_SD
)
summary(Post_Pene_combined_lm_Wider)##
## Call:
## lm(formula = Post_Pene_AVG ~ Site + Post_Burrow_Count + Pre_Pene_AVG +
## Pre_Live_SD * Post_Live_SD, data = Decomp_2018_Wider_2)
##
## Residuals:
## Min 1Q Median 3Q Max
## -16.3913 -4.6358 0.5382 5.0054 18.4769
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 7.773301 13.799515 0.563 0.5773
## Site -16.940539 6.328495 -2.677 0.0118 *
## Post_Burrow_Count -0.065593 0.232569 -0.282 0.7798
## Pre_Pene_AVG 0.277920 0.228463 1.216 0.2330
## Pre_Live_SD 0.566737 0.251426 2.254 0.0314 *
## Post_Live_SD 0.377614 0.274110 1.378 0.1782
## Pre_Live_SD:Post_Live_SD -0.010887 0.005602 -1.943 0.0611 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 8.934 on 31 degrees of freedom
## Multiple R-squared: 0.6752, Adjusted R-squared: 0.6123
## F-statistic: 10.74 on 6 and 31 DF, p-value: 1.881e-06#Burrows
Burrows_combined_NBglm_2 <- glm.nb(data = Decomp_2018_3,
Post_Burrow_Count ~
Density_Num *
Pre_Pene_AVG +
Site #+
#Pre_Live_SD
,
link = "log"
)
summary(Burrows_combined_NBglm_2)##
## Call:
## glm.nb(formula = Post_Burrow_Count ~ Density_Num * Pre_Pene_AVG +
## Site, data = Decomp_2018_3, link = "log", init.theta = 7.122816618)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -2.4164 -0.8842 -0.1185 0.4951 2.7355
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 1.0230109 0.2745335 3.726 0.000194 ***
## Density_Num -0.0354466 0.0154881 -2.289 0.022100 *
## Pre_Pene_AVG -0.0165901 0.0113395 -1.463 0.143457
## Site 2.1431015 0.1836969 11.667 < 2e-16 ***
## Density_Num:Pre_Pene_AVG 0.0037973 0.0009855 3.853 0.000117 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for Negative Binomial(7.1228) family taken to be 1)
##
## Null deviance: 369.40 on 84 degrees of freedom
## Residual deviance: 100.94 on 80 degrees of freedom
## AIC: 495.88
##
## Number of Fisher Scoring iterations: 1
##
##
## Theta: 7.12
## Std. Err.: 1.99
##
## 2 x log-likelihood: -483.88summary(glm.nb(data = combined_data_full_2017, Post_Burrow_Count ~ Density_Num * Pre_Pene_AVG + Site))##
## Call:
## glm.nb(formula = Post_Burrow_Count ~ Density_Num * Pre_Pene_AVG +
## Site, data = combined_data_full_2017, init.theta = 26.73567047,
## link = log)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -2.62162 -1.14612 -0.03518 0.62452 2.35427
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 0.024682 0.301902 0.082 0.935
## Density_Num 0.021463 0.015557 1.380 0.168
## Pre_Pene_AVG -0.012565 0.020513 -0.613 0.540
## Site 1.923375 0.214593 8.963 <2e-16 ***
## Density_Num:Pre_Pene_AVG 0.001686 0.001382 1.220 0.223
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for Negative Binomial(26.7357) family taken to be 1)
##
## Null deviance: 209.887 on 47 degrees of freedom
## Residual deviance: 64.718 on 43 degrees of freedom
## AIC: 217.74
##
## Number of Fisher Scoring iterations: 1
##
##
## Theta: 26.7
## Std. Err.: 36.5
##
## 2 x log-likelihood: -205.741summary(glm.nb(data = combined_data_full, Post_Burrow_Count ~ Density_Num * Pre_Pene_AVG + Site + Year))##
## Call:
## glm.nb(formula = Post_Burrow_Count ~ Density_Num * Pre_Pene_AVG +
## Site + Year, data = combined_data_full, init.theta = 6.930012647,
## link = log)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -2.6041 -0.9683 -0.1138 0.4572 2.6459
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 0.1904821 0.2521365 0.755 0.44997
## Density_Num -0.0085082 0.0136527 -0.623 0.53316
## Pre_Pene_AVG -0.0131145 0.0125118 -1.048 0.29456
## Site 1.9953157 0.1718184 11.613 < 2e-16 ***
## Year2018 0.7975175 0.1220847 6.532 6.47e-11 ***
## Density_Num:Pre_Pene_AVG 0.0026698 0.0009478 2.817 0.00485 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for Negative Binomial(6.93) family taken to be 1)
##
## Null deviance: 415.55 on 95 degrees of freedom
## Residual deviance: 118.46 on 90 degrees of freedom
## AIC: 506.87
##
## Number of Fisher Scoring iterations: 1
##
##
## Theta: 6.93
## Std. Err.: 2.14
##
## 2 x log-likelihood: -492.875#Initial Soil Strength
Pre_Pene_combined_lm_2 <- lm(data = Decomp_2018_3,
Pre_Pene_AVG ~
Site
)
summary(Pre_Pene_combined_lm_2)##
## Call:
## lm(formula = Pre_Pene_AVG ~ Site, data = Decomp_2018_3)
##
## Residuals:
## Min 1Q Median 3Q Max
## -11.5009 -5.3493 -0.3493 6.6507 11.8291
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 25.171 1.023 24.60 < 2e-16 ***
## Site -14.822 1.455 -10.18 2.84e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 6.709 on 83 degrees of freedom
## Multiple R-squared: 0.5554, Adjusted R-squared: 0.5501
## F-statistic: 103.7 on 1 and 83 DF, p-value: 2.845e-16#Spartina Biomass
SB_Gamma_glm_2 <- glm(data = Decomp_2018_3,
Spartina_Biomass ~
Post_Burrow_Count +
Pre_Live_SD *
Post_Live_SD +
Pre_Pene_AVG +
Density_Num +
Post_Live_SD *
Post_Pene_AVG +
Site,
family = Gamma(link = "log")
)
summary(SB_Gamma_glm_2)##
## Call:
## glm(formula = Spartina_Biomass ~ Post_Burrow_Count + Pre_Live_SD *
## Post_Live_SD + Pre_Pene_AVG + Density_Num + Post_Live_SD *
## Post_Pene_AVG + Site, family = Gamma(link = "log"), data = Decomp_2018_3)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -0.9402 -0.3029 -0.0478 0.1822 0.9958
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 4.9262151 0.5361895 9.187 6.56e-14 ***
## Post_Burrow_Count -0.0039837 0.0075642 -0.527 0.59999
## Pre_Live_SD 0.0033170 0.0092298 0.359 0.72032
## Post_Live_SD 0.0025826 0.0136624 0.189 0.85058
## Pre_Pene_AVG -0.0275342 0.0083477 -3.298 0.00149 **
## Density_Num 0.0231255 0.0076967 3.005 0.00361 **
## Post_Pene_AVG -0.0147094 0.0131761 -1.116 0.26783
## Site -0.8258862 0.2565610 -3.219 0.00190 **
## Pre_Live_SD:Post_Live_SD -0.0002100 0.0002132 -0.985 0.32765
## Post_Live_SD:Post_Pene_AVG 0.0003910 0.0003408 1.147 0.25494
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for Gamma family taken to be 0.1937281)
##
## Null deviance: 30.818 on 84 degrees of freedom
## Residual deviance: 15.346 on 75 degrees of freedom
## AIC: 799.84
##
## Number of Fisher Scoring iterations: 8#Decomposition
Decomp_lm_2 <- lm(data = Decomp_2018_3,
End_Mass_LB ~
Post_Burrow_Count *
Depth +
Pre_Pene_AVG +
Site
)
summary(Decomp_lm_2)##
## Call:
## lm(formula = End_Mass_LB ~ Post_Burrow_Count * Depth + Pre_Pene_AVG +
## Site, data = Decomp_2018_3)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.30003 -0.08816 -0.00647 0.09855 0.35219
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.7067886 0.0738410 9.572 7.47e-15 ***
## Post_Burrow_Count -0.0047980 0.0035313 -1.359 0.17810
## Depth 0.0069882 0.0044901 1.556 0.12362
## Pre_Pene_AVG -0.0069477 0.0022727 -3.057 0.00305 **
## Site -0.0715204 0.0634305 -1.128 0.26293
## Post_Burrow_Count:Depth 0.0006181 0.0002736 2.259 0.02662 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.1381 on 79 degrees of freedom
## Multiple R-squared: 0.3445, Adjusted R-squared: 0.303
## F-statistic: 8.303 on 5 and 79 DF, p-value: 2.415e-06#Final Spartina Density
SD_combined_NBglm_2 <- glm.nb(data = Decomp_2018_3,
Post_Live_SD ~
Post_Burrow_Count +
Pre_Live_SD +
Site +
Pre_Pene_AVG,
link = "log"
)
summary(SD_combined_NBglm_2)##
## Call:
## glm.nb(formula = Post_Live_SD ~ Post_Burrow_Count + Pre_Live_SD +
## Site + Pre_Pene_AVG, data = Decomp_2018_3, link = "log",
## init.theta = 10.76716907)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -2.19944 -0.55984 -0.01931 0.55373 2.35660
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 3.7172516 0.1924531 19.315 < 2e-16 ***
## Post_Burrow_Count 0.0006036 0.0058031 0.104 0.91716
## Pre_Live_SD 0.0070561 0.0025325 2.786 0.00533 **
## Site -0.2153832 0.1594510 -1.351 0.17677
## Pre_Pene_AVG -0.0123376 0.0056952 -2.166 0.03029 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for Negative Binomial(10.7672) family taken to be 1)
##
## Null deviance: 100.710 on 84 degrees of freedom
## Residual deviance: 87.168 on 80 degrees of freedom
## AIC: 698.19
##
## Number of Fisher Scoring iterations: 1
##
##
## Theta: 10.77
## Std. Err.: 2.10
##
## 2 x log-likelihood: -686.189#The combined SEM with Decomp
combined_SEM_2 <- psem(Post_Pene_combined_lm_2,
Pre_Pene_combined_lm_2,
Burrows_combined_NBglm_2,
SB_Gamma_glm_2,
Decomp_lm_2,
SD_combined_NBglm_2
)
summary(combined_SEM_2)##
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## Structural Equation Model of combined_SEM_2
##
## Call:
## Post_Pene_AVG ~ Site + Post_Burrow_Count + Pre_Pene_AVG + Pre_Live_SD * Post_Live_SD
## Pre_Pene_AVG ~ Site
## Post_Burrow_Count ~ Density_Num * Pre_Pene_AVG + Site
## Spartina_Biomass ~ Post_Burrow_Count + Pre_Live_SD * Post_Live_SD + Pre_Pene_AVG + Density_Num + Post_Live_SD * Post_Pene_AVG + Site
## End_Mass_LB ~ Post_Burrow_Count * Depth + Pre_Pene_AVG + Site
## Post_Live_SD ~ Post_Burrow_Count + Pre_Live_SD + Site + Pre_Pene_AVG
##
## AIC BIC
## 104.142 204.291
##
## ---
## Tests of directed separation:
##
## Independ.Claim Test.Type DF Crit.Value P.Value
## Pre_Pene_AVG ~ Pre_Live_SD + ... coef 82 -0.9445 0.3477
## Post_Burrow_Count ~ Pre_Live_SD + ... coef 79 -0.2743 0.7839
## End_Mass_LB ~ Pre_Live_SD + ... coef 78 0.1066 0.9154
## Pre_Pene_AVG ~ Density_Num + ... coef 82 -1.8133 0.0734
## Post_Pene_AVG ~ Density_Num + ... coef 77 -2.2963 0.0244 *
## Post_Live_SD ~ Density_Num + ... coef 79 -0.4757 0.6343
## End_Mass_LB ~ Density_Num + ... coef 78 0.0716 0.9431
## Pre_Pene_AVG ~ Depth + ... coef 82 0.1751 0.8615
## Post_Pene_AVG ~ Depth + ... coef 77 0.0742 0.9410
## Post_Burrow_Count ~ Depth + ... coef 79 -0.1225 0.9025
## Post_Live_SD ~ Depth + ... coef 79 -0.4178 0.6761
## Spartina_Biomass ~ Depth + ... coef 74 -0.3092 0.7580
## End_Mass_LB ~ Post_Pene_AVG + ... coef 75 0.1355 0.8926
## End_Mass_LB ~ Post_Live_SD + ... coef 77 -0.1754 0.8613
## Spartina_Biomass ~ End_Mass_LB + ... coef 72 -1.2876 0.2020
##
## Global goodness-of-fit:
##
## Fisher's C = 22.142 with P-value = 0.849 and on 30 degrees of freedom
##
## ---
## Coefficients:
##
## Response Predictor Estimate Std.Error DF Crit.Value
## Post_Pene_AVG Site -15.1818 3.8570 78 -3.9362
## Post_Pene_AVG Post_Burrow_Count -0.1502 0.1385 78 -1.0846
## Post_Pene_AVG Pre_Pene_AVG 0.2872 0.1391 78 2.0641
## Post_Pene_AVG Pre_Live_SD 0.5116 0.1585 78 3.2284
## Post_Pene_AVG Post_Live_SD 0.3751 0.1731 78 2.1668
## Post_Pene_AVG Pre_Live_SD:Post_Live_SD -0.0100 0.0036 78 -2.8060
## Pre_Pene_AVG Site -14.8216 1.4555 83 -10.1833
## Post_Burrow_Count Density_Num -0.0354 0.0155 80 -2.2886
## Post_Burrow_Count Pre_Pene_AVG -0.0166 0.0113 80 -1.4630
## Post_Burrow_Count Site 2.1431 0.1837 80 11.6665
## Post_Burrow_Count Density_Num:Pre_Pene_AVG 0.0038 0.0010 80 3.8533
## Spartina_Biomass Post_Burrow_Count -0.0040 0.0076 75 -0.5266
## Spartina_Biomass Pre_Live_SD 0.0033 0.0092 75 0.3594
## Spartina_Biomass Post_Live_SD 0.0026 0.0137 75 0.1890
## Spartina_Biomass Pre_Pene_AVG -0.0275 0.0083 75 -3.2984
## Spartina_Biomass Density_Num 0.0231 0.0077 75 3.0046
## Spartina_Biomass Post_Pene_AVG -0.0147 0.0132 75 -1.1164
## Spartina_Biomass Site -0.8259 0.2566 75 -3.2191
## Spartina_Biomass Pre_Live_SD:Post_Live_SD -0.0002 0.0002 75 -0.9853
## Spartina_Biomass Post_Live_SD:Post_Pene_AVG 0.0004 0.0003 75 1.1472
## End_Mass_LB Post_Burrow_Count -0.0048 0.0035 79 -1.3587
## End_Mass_LB Depth 0.0070 0.0045 79 1.5564
## End_Mass_LB Pre_Pene_AVG -0.0069 0.0023 79 -3.0570
## End_Mass_LB Site -0.0715 0.0634 79 -1.1275
## End_Mass_LB Post_Burrow_Count:Depth 0.0006 0.0003 79 2.2592
## Post_Live_SD Post_Burrow_Count 0.0006 0.0058 80 0.1040
## Post_Live_SD Pre_Live_SD 0.0071 0.0025 80 2.7863
## Post_Live_SD Site -0.2154 0.1595 80 -1.3508
## Post_Live_SD Pre_Pene_AVG -0.0123 0.0057 80 -2.1663
## P.Value Std.Estimate
## 0.0002 -0.5431 ***
## 0.2814 -0.1179
## 0.0423 0.2043 *
## 0.0018 0.5575 **
## 0.0333 0.3999 *
## 0.0063 -0.7691 **
## 0.0000 -0.7453 ***
## 0.0221 - *
## 0.1435 -
## 0.0000 - ***
## 0.0001 - ***
## 0.6000 -
## 0.7203 -
## 0.8506 -
## 0.0015 - **
## 0.0036 - **
## 0.2678 -
## 0.0019 - **
## 0.3276 -
## 0.2549 -
## 0.1781 -0.3202
## 0.1236 0.2121
## 0.0031 -0.4201 **
## 0.2629 -0.2175
## 0.0266 0.5154 *
## 0.9172 -
## 0.0053 - **
## 0.1768 -
## 0.0303 - *
##
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05
##
## ---
## Individual R-squared:
##
## Response method R.squared
## Post_Pene_AVG none 0.69
## Pre_Pene_AVG none 0.56
## Post_Burrow_Count nagelkerke 0.97
## Spartina_Biomass nagelkerke 0.55
## End_Mass_LB none 0.34
## Post_Live_SD nagelkerke 0.21summary(combined_SEM)##
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## Structural Equation Model of combined_SEM
##
## Call:
## Post_Pene_AVG ~ Post_Burrow_Count + Pre_Pene_AVG + Site + Year_Fac + Pre_Live_SD * Post_Live_SD
## Post_Burrow_Count ~ Density_Num * Pre_Pene_AVG + Year_Fac + Site
## Spartina_Biomass ~ Pre_Live_SD * Post_Live_SD + Post_Burrow_Count * Pre_Pene_AVG + Density_Num + Site + Year_Fac
## Post_Live_SD ~ Density_Num + Post_Burrow_Count + Pre_Live_SD + Pre_Pene_AVG + Site + Year_Fac
## Pre_Pene_AVG ~ Site + Year_Fac
##
## AIC BIC
## 91.032 191.042
##
## ---
## Tests of directed separation:
##
## Independ.Claim Test.Type DF Crit.Value P.Value
## Pre_Pene_AVG ~ Pre_Live_SD + ... coef 92 -1.0718 0.2866
## Post_Burrow_Count ~ Pre_Live_SD + ... coef 89 -1.6348 0.1021
## Pre_Pene_AVG ~ Density_Num + ... coef 92 -0.7572 0.4508
## Post_Pene_AVG ~ Density_Num + ... coef 87 -0.4998 0.6185
## Spartina_Biomass ~ Post_Pene_AVG + ... coef 85 -1.3477 0.1813
##
## Global goodness-of-fit:
##
## Fisher's C = 13.032 with P-value = 0.222 and on 10 degrees of freedom
##
## ---
## Coefficients:
##
## Response Predictor Estimate Std.Error DF
## Post_Pene_AVG Post_Burrow_Count -0.3511 0.1412 88
## Post_Pene_AVG Pre_Pene_AVG 0.3039 0.1147 88
## Post_Pene_AVG Site -9.9324 3.0134 88
## Post_Pene_AVG Year_Fac -0.4286 3.2513 88
## Post_Pene_AVG Pre_Live_SD 0.3268 0.1032 88
## Post_Pene_AVG Post_Live_SD 0.1930 0.1248 88
## Post_Pene_AVG Pre_Live_SD:Post_Live_SD -0.0062 0.0024 88
## Post_Burrow_Count Density_Num -0.0085 0.0137 90
## Post_Burrow_Count Pre_Pene_AVG -0.0131 0.0125 90
## Post_Burrow_Count Year_Fac -0.7975 0.1221 90
## Post_Burrow_Count Site 1.9953 0.1718 90
## Post_Burrow_Count Density_Num:Pre_Pene_AVG 0.0027 0.0009 90
## Spartina_Biomass Pre_Live_SD 0.0228 0.0075 86
## Spartina_Biomass Post_Live_SD 0.0360 0.0091 86
## Spartina_Biomass Post_Burrow_Count 0.0047 0.0156 86
## Spartina_Biomass Pre_Pene_AVG -0.0319 0.0108 86
## Spartina_Biomass Density_Num 0.0071 0.0087 86
## Spartina_Biomass Site -1.2738 0.2203 86
## Spartina_Biomass Year_Fac -0.2153 0.2340 86
## Spartina_Biomass Pre_Live_SD:Post_Live_SD -0.0006 0.0002 86
## Spartina_Biomass Post_Burrow_Count:Pre_Pene_AVG 0.0002 0.0009 86
## Post_Live_SD Density_Num -0.0028 0.0062 89
## Post_Live_SD Post_Burrow_Count -0.0008 0.0072 89
## Post_Live_SD Pre_Live_SD 0.0131 0.0033 89
## Post_Live_SD Pre_Pene_AVG -0.0081 0.0061 89
## Post_Live_SD Site -0.1383 0.1618 89
## Post_Live_SD Year_Fac -0.8989 0.1407 89
## Pre_Pene_AVG Site -12.6669 1.4545 93
## Pre_Pene_AVG Year_Fac -5.3335 1.4545 93
## Crit.Value P.Value Std.Estimate
## -2.4869 0.0148 -0.2713 *
## 2.6499 0.0095 0.2519 **
## -3.2961 0.0014 -0.4192 **
## -0.1318 0.8954 -0.0181
## 3.1681 0.0021 0.5226 **
## 1.5462 0.1256 0.3041
## -2.5296 0.0132 -0.6179 *
## -0.6232 0.5332 -
## -1.0482 0.2946 -
## -6.5325 0.0000 - ***
## 11.6129 0.0000 - ***
## 2.8167 0.0049 - **
## 3.0581 0.0030 - **
## 3.9664 0.0002 - ***
## 0.3048 0.7613 -
## -2.9493 0.0041 - **
## 0.8152 0.4172 -
## -5.7814 0.0000 - ***
## -0.9202 0.3600 -
## -3.6248 0.0005 - ***
## 0.1667 0.8680 -
## -0.4509 0.6520 -
## -0.1125 0.9104 -
## 3.9808 0.0001 - ***
## -1.3296 0.1837 -
## -0.8547 0.3927 -
## -6.3871 0.0000 - ***
## -8.7087 0.0000 -0.645 ***
## -3.6669 0.0004 -0.2716 ***
##
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05
##
## ---
## Individual R-squared:
##
## Response method R.squared
## Post_Pene_AVG none 0.61
## Post_Burrow_Count nagelkerke 0.97
## Spartina_Biomass nagelkerke 0.34
## Post_Live_SD nagelkerke 0.93
## Pre_Pene_AVG none 0.49Decomposition DAGs
## Piecewise SEM Decomposition DAG
plot(combined_SEM_2, show = "Estimate")## DiagrammeR Decomposition DAGs
### With Site
grViz("digraph Soil_Strength {
# a 'graph' statement
graph [overlap = false,
fontsize = 14]
# several 'node' statements
# Exogenous Variables
node [shape = rectangle,
fontname = Helvetica,
width = 1.3,
fontcolor = darkslategray,
color = darkslategray,
nodesep = 1,
penwidth = 2]
Crab_Density [label = '@@1']
Site [label = '@@5']
Depth [label = '@@12']
Burrow_Depth_Intrctn [label = '@@13']
# Endogenous Variables
node [shape = rectangle,
fixedsize = true,
width = 1.8,
color = steelblue,
fontcolor = darkslategray,
penwidth = 2]
Burrow_Density [label = '@@3']
Initial_SS [label = '@@4', color = darkslategray]
Final_SS [label = '@@6']
Depth [label = '@@12', color = SaddleBrown]
Burrow_Depth_Intrctn [label = '@@13', color = SaddleBrown]
End_Mass_LB [label = '@@14', color = SaddleBrown]
# Soil Strength Interaction
node [shape = rectangle,
fixedsize = true,
width = 2,
height = 0.9,
color = steelblue,
fontcolor = darkslategray,
penwidth = 2]
CrabSoil_Intrctn [label = '@@2']
# Primary Production
node [shape = rectangle,
fixedsize = true,
width = 2,
color = forestgreen,
fontcolor = darkslategray,
penwidth = 2]
Pre_Live_SD [label = '@@7']
Spartina_Biomass [label = '@@8']
Post_Live_SD [label = '@@9']
Pre_post_Intrctn [label = '@@10', height = 0.9, width = 2.3]
# Soil Shoots Interaction
node [shape = rectangle,
fixedsize = true,
width = 2.2,
height = 0.9,
color = CadetBlue,
fontcolor = darkslategray,
penwidth = 2]
SoilShoots_Intrctn [label = '@@11']
# several 'edge' statements
#Soil Strength Exogenous Variables
edge [color = grey, arrowhead = normal, penwidth = 1, minlen = 3]
Initial_SS->Burrow_Density
Crab_Density->Burrow_Density
Initial_SS->Spartina_Biomass
#Primary Production Exogenous Variables
edge [color = forestgreen, arrowhead = normal, penwidth = 5, minlen = 3]
Pre_Live_SD -> Final_SS
Pre_Live_SD -> Spartina_Biomass
Pre_Live_SD -> Post_Live_SD
Pre_post_Intrctn -> Spartina_Biomass
Pre_post_Intrctn -> Final_SS
Burrow_Density -> Spartina_Biomass [color = grey, arrowhead = normal, penwidth = 1, minlen = 3]
Final_SS -> Spartina_Biomass [color = grey, arrowhead = normal, penwidth = 1, minlen = 3]
Burrow_Density -> Post_Live_SD [color = grey, arrowhead = normal, penwidth = 1, minlen = 3]
Initial_SS -> End_Mass_LB [color = SaddleBrown] #was dimgrey
#All Endogenous Variables
edge [color = DimGray, arrowhead = normal, penwidth = 5, minlen = 5]
Site->Burrow_Density
Burrow_Density->Final_SS [color = steelblue]
Site->Initial_SS
Site->Final_SS
Initial_SS->Final_SS
Post_Live_SD->Spartina_Biomass [color = forestgreen]
Site -> Spartina_Biomass
Site->Post_Live_SD [color = grey, arrowhead = normal, penwidth = 1, minlen = 3]
Depth -> End_Mass_LB [color = grey, arrowhead = normal, penwidth = 1, minlen = 3]
Burrow_Depth_Intrctn -> End_Mass_LB [color = SaddleBrown]
Burrow_Density -> End_Mass_LB [color = SaddleBrown]
edge [color = steelblue, arrowhead = normal, penwidth = 5, minlen = 4]
CrabSoil_Intrctn->Burrow_Density
edge [color = CadetBlue arrowhead = normal, penwidth = 5, minlen = 4]
SoilShoots_Intrctn->Spartina_Biomass
}
[1]: 'Crab Density'
[2]: 'Crab Density and\\nInitial Soil Strength\\nInteraction\\n'
[3]: 'Burrow Density'
[4]: 'Initial Soil Strength'
[5]: 'Site'
[6]: 'Final Soil Strength'
[7]: 'Initial Shoot Density'
[8]: 'Spartina Biomass'
[9]: 'Final Shoot Density'
[10]: 'Initial Shoot Density and\\nFinal Shoot Density\\nInteraction\\n'
[11]: 'Final Soil Strength and\\nFinal Shoot Density\\nInteraction\\n'
[12]: 'Depth'
[13]: 'Burrow Density and\\nDepth Interaction\\n'
[14]: 'Final Litterbag Mass'
"
) ### Without Site
grViz("digraph Soil_Strength {
# a 'graph' statement
graph [overlap = false,
fontsize = 14]
# several 'node' statements
# Exogenous Variables
node [shape = rectangle,
fontname = Helvetica,
width = 1.3,
fontcolor = darkslategray,
color = darkslategray,
nodesep = 1,
penwidth = 2]
Crab_Density [label = '@@1']
Depth [label = '@@11', color = SaddleBrown]
Burrow_Depth_Intrctn [label = '@@12', color = SaddleBrown]
# Endogenous Variables
node [shape = rectangle,
fixedsize = true,
width = 1.8,
color = steelblue,
fontcolor = darkslategray,
penwidth = 2]
Burrow_Density [label = '@@3']
Initial_SS [label = '@@4', color = darkslategray]
Final_SS [label = '@@5']
End_Mass_LB [label = '@@13', color = SaddleBrown]
# Soil Strength Interaction
node [shape = rectangle,
fixedsize = true,
width = 2,
height = 0.9,
color = steelblue,
fontcolor = darkslategray,
penwidth = 2]
CrabSoil_Intrctn [label = '@@2']
# Primary Production
node [shape = rectangle,
fixedsize = true,
width = 2,
color = forestgreen,
fontcolor = darkslategray,
penwidth = 2]
Pre_Live_SD [label = '@@6']
Spartina_Biomass [label = '@@7']
Post_Live_SD [label = '@@8']
Pre_post_Intrctn [label = '@@9', height = 0.9, width = 2.3]
# Soil Shoots Interaction
node [shape = rectangle,
fixedsize = true,
width = 2.2,
height = 0.9,
color = CadetBlue,
fontcolor = darkslategray,
penwidth = 2]
SoilShoots_Intrctn [label = '@@10']
# several 'edge' statements
#Soil Strength Exogenous Variables
edge [color = grey, arrowhead = normal, penwidth = 1, minlen = 3]
Initial_SS->Burrow_Density
Crab_Density->Burrow_Density
Initial_SS->Spartina_Biomass
#Primary Production Exogenous Variables
edge [color = forestgreen, arrowhead = normal, penwidth = 5, minlen = 3]
Pre_Live_SD -> Final_SS
Pre_Live_SD -> Spartina_Biomass
Pre_Live_SD -> Post_Live_SD
Pre_post_Intrctn -> Spartina_Biomass
Pre_post_Intrctn -> Final_SS
Burrow_Density -> Spartina_Biomass [color = grey, arrowhead = normal, penwidth = 1, minlen = 3]
Final_SS -> Spartina_Biomass [color = grey, arrowhead = normal, penwidth = 1, minlen = 3]
Burrow_Density -> Post_Live_SD [color = grey, arrowhead = normal, penwidth = 1, minlen = 3]
Initial_SS -> End_Mass_LB [color = SaddleBrown] #Was DimGrey
#All Endogenous Variables
edge [color = DimGray, arrowhead = normal, penwidth = 5, minlen = 5]
Burrow_Density->Final_SS [color = steelblue]
Initial_SS->Final_SS
Post_Live_SD->Spartina_Biomass [color = forestgreen]
Depth -> End_Mass_LB [color = grey, arrowhead = normal, penwidth = 1, minlen = 3]
Burrow_Depth_Intrctn -> End_Mass_LB [color = SaddleBrown]
Burrow_Density -> End_Mass_LB [color = SaddleBrown]
edge [color = steelblue, arrowhead = normal, penwidth = 5, minlen = 4]
CrabSoil_Intrctn->Burrow_Density
edge [color = CadetBlue arrowhead = normal, penwidth = 5, minlen = 4]
SoilShoots_Intrctn->Spartina_Biomass
}
[1]: 'Crab Density'
[2]: 'Crab Density and\\nInitial Soil Strength\\nInteraction\\n'
[3]: 'Burrow Density'
[4]: 'Initial Soil Strength'
[5]: 'Final Soil Strength'
[6]: 'Initial Shoot Density'
[7]: 'Spartina Biomass'
[8]: 'Final Shoot Density'
[9]: 'Initial Shoot Density and\\nFinal Shoot Density\\nInteraction\\n'
[10]: 'Final Soil Strength and\\nFinal Shoot Density\\nInteraction\\n'
[11]: 'Depth'
[12]: 'Burrow Density and\\nDepth Interaction\\n'
[13]: 'Final Litterbag Mass'
"
) Decomposition Visreg
visreg::visreg2d(Decomp_lm_2,
"Depth",
"Post_Burrow_Count",
#scale = "response",
main = "Decomposition Rate",
#by = "Density_Num",
#breaks = c(0, 4, 8, 12, 16, 20),
ylab = "Final Burrow Density",
xlab = "Initial Depth"#,
#plot.type = "rgl"
)
visreg::visreg2d(Decomp_lm_2,
"Post_Burrow_Count",
"Depth",
#scale = "response",
#main = "Decomposition Rate",
#by = "Density_Num",
#breaks = c(0, 4, 8, 12, 16, 20),
ylab = "Final Burrow Density",
xlab = "Initial Depth",
plot.type = "rgl"
)## Loading required namespace: rgl#visreg::visreg(Decomp_lm_2,
#"Post_Burrow_Count",
#scale = "response",
#by = c("Depth", "Site"),
#breaks = c(0, 4, 8, 12, 16, 20),
#ylab = "Decomposition Rate",
#xlab = "Final Burrow Density"
#)New Decomposition Models
#Building the Models
#Soil Strength
Post_Pene_combined_lm_3 <- lm(data = Decomp_2018_3,
Post_Pene_AVG ~
Site +
Post_Burrow_Count +
Pre_Pene_AVG #+
#Pre_Live_SD *
#Post_Live_SD
)
summary(Post_Pene_combined_lm_3)##
## Call:
## lm(formula = Post_Pene_AVG ~ Site + Post_Burrow_Count + Pre_Pene_AVG,
## data = Decomp_2018_3)
##
## Residuals:
## Min 1Q Median 3Q Max
## -22.0632 -4.2702 -0.2899 2.6588 21.7954
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 27.7342 3.7703 7.356 1.38e-10 ***
## Site -14.6778 3.9387 -3.727 0.000358 ***
## Post_Burrow_Count -0.1642 0.1443 -1.138 0.258596
## Pre_Pene_AVG 0.2957 0.1412 2.094 0.039381 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 8.582 on 81 degrees of freedom
## Multiple R-squared: 0.6407, Adjusted R-squared: 0.6274
## F-statistic: 48.15 on 3 and 81 DF, p-value: < 2.2e-16#Wider Data
Post_Pene_combined_lm_Wider_2 <- lm(data = Decomp_2018_Wider_2,
Post_Pene_AVG ~
Site +
Post_Burrow_Count +
Pre_Pene_AVG +
Pre_Live_SD *
Post_Live_SD
)
summary(Post_Pene_combined_lm_Wider_2)##
## Call:
## lm(formula = Post_Pene_AVG ~ Site + Post_Burrow_Count + Pre_Pene_AVG +
## Pre_Live_SD * Post_Live_SD, data = Decomp_2018_Wider_2)
##
## Residuals:
## Min 1Q Median 3Q Max
## -16.3913 -4.6358 0.5382 5.0054 18.4769
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 7.773301 13.799515 0.563 0.5773
## Site -16.940539 6.328495 -2.677 0.0118 *
## Post_Burrow_Count -0.065593 0.232569 -0.282 0.7798
## Pre_Pene_AVG 0.277920 0.228463 1.216 0.2330
## Pre_Live_SD 0.566737 0.251426 2.254 0.0314 *
## Post_Live_SD 0.377614 0.274110 1.378 0.1782
## Pre_Live_SD:Post_Live_SD -0.010887 0.005602 -1.943 0.0611 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 8.934 on 31 degrees of freedom
## Multiple R-squared: 0.6752, Adjusted R-squared: 0.6123
## F-statistic: 10.74 on 6 and 31 DF, p-value: 1.881e-06#Burrows
Burrows_combined_NBglm_3 <- glm.nb(data = Decomp_2018_3,
Post_Burrow_Count ~
Density_Num *
Pre_Pene_AVG +
Site #+
#Pre_Live_SD
,
link = "log"
)
summary(Burrows_combined_NBglm_3)##
## Call:
## glm.nb(formula = Post_Burrow_Count ~ Density_Num * Pre_Pene_AVG +
## Site, data = Decomp_2018_3, link = "log", init.theta = 7.122816618)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -2.4164 -0.8842 -0.1185 0.4951 2.7355
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 1.0230109 0.2745335 3.726 0.000194 ***
## Density_Num -0.0354466 0.0154881 -2.289 0.022100 *
## Pre_Pene_AVG -0.0165901 0.0113395 -1.463 0.143457
## Site 2.1431015 0.1836969 11.667 < 2e-16 ***
## Density_Num:Pre_Pene_AVG 0.0037973 0.0009855 3.853 0.000117 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for Negative Binomial(7.1228) family taken to be 1)
##
## Null deviance: 369.40 on 84 degrees of freedom
## Residual deviance: 100.94 on 80 degrees of freedom
## AIC: 495.88
##
## Number of Fisher Scoring iterations: 1
##
##
## Theta: 7.12
## Std. Err.: 1.99
##
## 2 x log-likelihood: -483.88summary(glm.nb(data = combined_data_full_2017, Post_Burrow_Count ~ Density_Num * Pre_Pene_AVG + Site))##
## Call:
## glm.nb(formula = Post_Burrow_Count ~ Density_Num * Pre_Pene_AVG +
## Site, data = combined_data_full_2017, init.theta = 26.73567047,
## link = log)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -2.62162 -1.14612 -0.03518 0.62452 2.35427
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 0.024682 0.301902 0.082 0.935
## Density_Num 0.021463 0.015557 1.380 0.168
## Pre_Pene_AVG -0.012565 0.020513 -0.613 0.540
## Site 1.923375 0.214593 8.963 <2e-16 ***
## Density_Num:Pre_Pene_AVG 0.001686 0.001382 1.220 0.223
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for Negative Binomial(26.7357) family taken to be 1)
##
## Null deviance: 209.887 on 47 degrees of freedom
## Residual deviance: 64.718 on 43 degrees of freedom
## AIC: 217.74
##
## Number of Fisher Scoring iterations: 1
##
##
## Theta: 26.7
## Std. Err.: 36.5
##
## 2 x log-likelihood: -205.741summary(glm.nb(data = combined_data_full, Post_Burrow_Count ~ Density_Num * Pre_Pene_AVG + Site + Year))##
## Call:
## glm.nb(formula = Post_Burrow_Count ~ Density_Num * Pre_Pene_AVG +
## Site + Year, data = combined_data_full, init.theta = 6.930012647,
## link = log)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -2.6041 -0.9683 -0.1138 0.4572 2.6459
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 0.1904821 0.2521365 0.755 0.44997
## Density_Num -0.0085082 0.0136527 -0.623 0.53316
## Pre_Pene_AVG -0.0131145 0.0125118 -1.048 0.29456
## Site 1.9953157 0.1718184 11.613 < 2e-16 ***
## Year2018 0.7975175 0.1220847 6.532 6.47e-11 ***
## Density_Num:Pre_Pene_AVG 0.0026698 0.0009478 2.817 0.00485 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for Negative Binomial(6.93) family taken to be 1)
##
## Null deviance: 415.55 on 95 degrees of freedom
## Residual deviance: 118.46 on 90 degrees of freedom
## AIC: 506.87
##
## Number of Fisher Scoring iterations: 1
##
##
## Theta: 6.93
## Std. Err.: 2.14
##
## 2 x log-likelihood: -492.875#Initial Soil Strength
Pre_Pene_combined_lm_3 <- lm(data = Decomp_2018_3,
Pre_Pene_AVG ~
Site
)
summary(Pre_Pene_combined_lm_3)##
## Call:
## lm(formula = Pre_Pene_AVG ~ Site, data = Decomp_2018_3)
##
## Residuals:
## Min 1Q Median 3Q Max
## -11.5009 -5.3493 -0.3493 6.6507 11.8291
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 25.171 1.023 24.60 < 2e-16 ***
## Site -14.822 1.455 -10.18 2.84e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 6.709 on 83 degrees of freedom
## Multiple R-squared: 0.5554, Adjusted R-squared: 0.5501
## F-statistic: 103.7 on 1 and 83 DF, p-value: 2.845e-16#Spartina Biomass
SB_Gamma_glm_3 <- glm(data = Decomp_2018_3,
Spartina_Biomass ~
Post_Burrow_Count +
Pre_Live_SD *
Post_Live_SD +
Pre_Pene_AVG +
Density_Num +
Post_Live_SD *
Post_Pene_AVG +
Site,
family = Gamma(link = "log")
)
summary(SB_Gamma_glm_3)##
## Call:
## glm(formula = Spartina_Biomass ~ Post_Burrow_Count + Pre_Live_SD *
## Post_Live_SD + Pre_Pene_AVG + Density_Num + Post_Live_SD *
## Post_Pene_AVG + Site, family = Gamma(link = "log"), data = Decomp_2018_3)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -0.9402 -0.3029 -0.0478 0.1822 0.9958
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 4.9262151 0.5361895 9.187 6.56e-14 ***
## Post_Burrow_Count -0.0039837 0.0075642 -0.527 0.59999
## Pre_Live_SD 0.0033170 0.0092298 0.359 0.72032
## Post_Live_SD 0.0025826 0.0136624 0.189 0.85058
## Pre_Pene_AVG -0.0275342 0.0083477 -3.298 0.00149 **
## Density_Num 0.0231255 0.0076967 3.005 0.00361 **
## Post_Pene_AVG -0.0147094 0.0131761 -1.116 0.26783
## Site -0.8258862 0.2565610 -3.219 0.00190 **
## Pre_Live_SD:Post_Live_SD -0.0002100 0.0002132 -0.985 0.32765
## Post_Live_SD:Post_Pene_AVG 0.0003910 0.0003408 1.147 0.25494
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for Gamma family taken to be 0.1937281)
##
## Null deviance: 30.818 on 84 degrees of freedom
## Residual deviance: 15.346 on 75 degrees of freedom
## AIC: 799.84
##
## Number of Fisher Scoring iterations: 8#Decomposition
Decomp_lm_3 <- lm(data = Decomp_2018_3,
End_Mass_LB ~
Post_Burrow_Count *
Depth +
Pre_Pene_AVG +
Site
)
summary(Decomp_lm_3)##
## Call:
## lm(formula = End_Mass_LB ~ Post_Burrow_Count * Depth + Pre_Pene_AVG +
## Site, data = Decomp_2018_3)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.30003 -0.08816 -0.00647 0.09855 0.35219
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.7067886 0.0738410 9.572 7.47e-15 ***
## Post_Burrow_Count -0.0047980 0.0035313 -1.359 0.17810
## Depth 0.0069882 0.0044901 1.556 0.12362
## Pre_Pene_AVG -0.0069477 0.0022727 -3.057 0.00305 **
## Site -0.0715204 0.0634305 -1.128 0.26293
## Post_Burrow_Count:Depth 0.0006181 0.0002736 2.259 0.02662 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.1381 on 79 degrees of freedom
## Multiple R-squared: 0.3445, Adjusted R-squared: 0.303
## F-statistic: 8.303 on 5 and 79 DF, p-value: 2.415e-06#Final Spartina Density
SD_combined_NBglm_3 <- glm.nb(data = Decomp_2018_3,
Post_Live_SD ~
Post_Burrow_Count +
Pre_Live_SD +
Site +
Pre_Pene_AVG,
link = "log"
)
summary(SD_combined_NBglm_3)##
## Call:
## glm.nb(formula = Post_Live_SD ~ Post_Burrow_Count + Pre_Live_SD +
## Site + Pre_Pene_AVG, data = Decomp_2018_3, link = "log",
## init.theta = 10.76716907)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -2.19944 -0.55984 -0.01931 0.55373 2.35660
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 3.7172516 0.1924531 19.315 < 2e-16 ***
## Post_Burrow_Count 0.0006036 0.0058031 0.104 0.91716
## Pre_Live_SD 0.0070561 0.0025325 2.786 0.00533 **
## Site -0.2153832 0.1594510 -1.351 0.17677
## Pre_Pene_AVG -0.0123376 0.0056952 -2.166 0.03029 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for Negative Binomial(10.7672) family taken to be 1)
##
## Null deviance: 100.710 on 84 degrees of freedom
## Residual deviance: 87.168 on 80 degrees of freedom
## AIC: 698.19
##
## Number of Fisher Scoring iterations: 1
##
##
## Theta: 10.77
## Std. Err.: 2.10
##
## 2 x log-likelihood: -686.189#The combined SEM with Decomp
combined_SEM_3 <- psem(#Post_Pene_combined_lm_3,
Pre_Pene_combined_lm_3,
Burrows_combined_NBglm_3,
#SB_Gamma_glm_3,
Decomp_lm_3#,
#SD_combined_NBglm_3
)
summary(combined_SEM_3)##
|
| | 0%
|
|================== | 25%
|
|=================================== | 50%
|
|==================================================== | 75%
|
|======================================================================| 100%##
## Structural Equation Model of combined_SEM_3
##
## Call:
## Pre_Pene_AVG ~ Site
## Post_Burrow_Count ~ Density_Num * Pre_Pene_AVG + Site
## End_Mass_LB ~ Post_Burrow_Count * Depth + Pre_Pene_AVG + Site
##
## AIC BIC
## 37.843 76.925
##
## ---
## Tests of directed separation:
##
## Independ.Claim Test.Type DF Crit.Value P.Value
## Pre_Pene_AVG ~ Density_Num + ... coef 82 -1.8133 0.0734
## End_Mass_LB ~ Density_Num + ... coef 78 0.0716 0.9431
## Pre_Pene_AVG ~ Depth + ... coef 82 0.1751 0.8615
## Post_Burrow_Count ~ Depth + ... coef 79 -0.1225 0.9025
##
## Global goodness-of-fit:
##
## Fisher's C = 5.843 with P-value = 0.665 and on 8 degrees of freedom
##
## ---
## Coefficients:
##
## Response Predictor Estimate Std.Error DF Crit.Value
## Pre_Pene_AVG Site -14.8216 1.4555 83 -10.1833
## Post_Burrow_Count Density_Num -0.0354 0.0155 80 -2.2886
## Post_Burrow_Count Pre_Pene_AVG -0.0166 0.0113 80 -1.4630
## Post_Burrow_Count Site 2.1431 0.1837 80 11.6665
## Post_Burrow_Count Density_Num:Pre_Pene_AVG 0.0038 0.0010 80 3.8533
## End_Mass_LB Post_Burrow_Count -0.0048 0.0035 79 -1.3587
## End_Mass_LB Depth 0.0070 0.0045 79 1.5564
## End_Mass_LB Pre_Pene_AVG -0.0069 0.0023 79 -3.0570
## End_Mass_LB Site -0.0715 0.0634 79 -1.1275
## End_Mass_LB Post_Burrow_Count:Depth 0.0006 0.0003 79 2.2592
## P.Value Std.Estimate
## 0.0000 -0.7453 ***
## 0.0221 - *
## 0.1435 -
## 0.0000 - ***
## 0.0001 - ***
## 0.1781 -0.3202
## 0.1236 0.2121
## 0.0031 -0.4201 **
## 0.2629 -0.2175
## 0.0266 0.5154 *
##
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05
##
## ---
## Individual R-squared:
##
## Response method R.squared
## Pre_Pene_AVG none 0.56
## Post_Burrow_Count nagelkerke 0.97
## End_Mass_LB none 0.34summary(combined_SEM)##
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## Structural Equation Model of combined_SEM
##
## Call:
## Post_Pene_AVG ~ Post_Burrow_Count + Pre_Pene_AVG + Site + Year_Fac + Pre_Live_SD * Post_Live_SD
## Post_Burrow_Count ~ Density_Num * Pre_Pene_AVG + Year_Fac + Site
## Spartina_Biomass ~ Pre_Live_SD * Post_Live_SD + Post_Burrow_Count * Pre_Pene_AVG + Density_Num + Site + Year_Fac
## Post_Live_SD ~ Density_Num + Post_Burrow_Count + Pre_Live_SD + Pre_Pene_AVG + Site + Year_Fac
## Pre_Pene_AVG ~ Site + Year_Fac
##
## AIC BIC
## 91.032 191.042
##
## ---
## Tests of directed separation:
##
## Independ.Claim Test.Type DF Crit.Value P.Value
## Pre_Pene_AVG ~ Pre_Live_SD + ... coef 92 -1.0718 0.2866
## Post_Burrow_Count ~ Pre_Live_SD + ... coef 89 -1.6348 0.1021
## Pre_Pene_AVG ~ Density_Num + ... coef 92 -0.7572 0.4508
## Post_Pene_AVG ~ Density_Num + ... coef 87 -0.4998 0.6185
## Spartina_Biomass ~ Post_Pene_AVG + ... coef 85 -1.3477 0.1813
##
## Global goodness-of-fit:
##
## Fisher's C = 13.032 with P-value = 0.222 and on 10 degrees of freedom
##
## ---
## Coefficients:
##
## Response Predictor Estimate Std.Error DF
## Post_Pene_AVG Post_Burrow_Count -0.3511 0.1412 88
## Post_Pene_AVG Pre_Pene_AVG 0.3039 0.1147 88
## Post_Pene_AVG Site -9.9324 3.0134 88
## Post_Pene_AVG Year_Fac -0.4286 3.2513 88
## Post_Pene_AVG Pre_Live_SD 0.3268 0.1032 88
## Post_Pene_AVG Post_Live_SD 0.1930 0.1248 88
## Post_Pene_AVG Pre_Live_SD:Post_Live_SD -0.0062 0.0024 88
## Post_Burrow_Count Density_Num -0.0085 0.0137 90
## Post_Burrow_Count Pre_Pene_AVG -0.0131 0.0125 90
## Post_Burrow_Count Year_Fac -0.7975 0.1221 90
## Post_Burrow_Count Site 1.9953 0.1718 90
## Post_Burrow_Count Density_Num:Pre_Pene_AVG 0.0027 0.0009 90
## Spartina_Biomass Pre_Live_SD 0.0228 0.0075 86
## Spartina_Biomass Post_Live_SD 0.0360 0.0091 86
## Spartina_Biomass Post_Burrow_Count 0.0047 0.0156 86
## Spartina_Biomass Pre_Pene_AVG -0.0319 0.0108 86
## Spartina_Biomass Density_Num 0.0071 0.0087 86
## Spartina_Biomass Site -1.2738 0.2203 86
## Spartina_Biomass Year_Fac -0.2153 0.2340 86
## Spartina_Biomass Pre_Live_SD:Post_Live_SD -0.0006 0.0002 86
## Spartina_Biomass Post_Burrow_Count:Pre_Pene_AVG 0.0002 0.0009 86
## Post_Live_SD Density_Num -0.0028 0.0062 89
## Post_Live_SD Post_Burrow_Count -0.0008 0.0072 89
## Post_Live_SD Pre_Live_SD 0.0131 0.0033 89
## Post_Live_SD Pre_Pene_AVG -0.0081 0.0061 89
## Post_Live_SD Site -0.1383 0.1618 89
## Post_Live_SD Year_Fac -0.8989 0.1407 89
## Pre_Pene_AVG Site -12.6669 1.4545 93
## Pre_Pene_AVG Year_Fac -5.3335 1.4545 93
## Crit.Value P.Value Std.Estimate
## -2.4869 0.0148 -0.2713 *
## 2.6499 0.0095 0.2519 **
## -3.2961 0.0014 -0.4192 **
## -0.1318 0.8954 -0.0181
## 3.1681 0.0021 0.5226 **
## 1.5462 0.1256 0.3041
## -2.5296 0.0132 -0.6179 *
## -0.6232 0.5332 -
## -1.0482 0.2946 -
## -6.5325 0.0000 - ***
## 11.6129 0.0000 - ***
## 2.8167 0.0049 - **
## 3.0581 0.0030 - **
## 3.9664 0.0002 - ***
## 0.3048 0.7613 -
## -2.9493 0.0041 - **
## 0.8152 0.4172 -
## -5.7814 0.0000 - ***
## -0.9202 0.3600 -
## -3.6248 0.0005 - ***
## 0.1667 0.8680 -
## -0.4509 0.6520 -
## -0.1125 0.9104 -
## 3.9808 0.0001 - ***
## -1.3296 0.1837 -
## -0.8547 0.3927 -
## -6.3871 0.0000 - ***
## -8.7087 0.0000 -0.645 ***
## -3.6669 0.0004 -0.2716 ***
##
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05
##
## ---
## Individual R-squared:
##
## Response method R.squared
## Post_Pene_AVG none 0.61
## Post_Burrow_Count nagelkerke 0.97
## Spartina_Biomass nagelkerke 0.34
## Post_Live_SD nagelkerke 0.93
## Pre_Pene_AVG none 0.49plot(SS_Model, show = "STD")plot(combined_SEM_3, show = "STD")New Decomposition DAGs
## Piecewise SEM Decomposition DAG
plot(combined_SEM_3, show = "Estimate")## DiagrammeR Decomposition DAGs
### With Site
grViz("digraph Soil_Strength {
# a 'graph' statement
graph [overlap = false,
fontsize = 14]
# several 'node' statements
# Exogenous Variables
node [shape = rectangle,
fontname = Helvetica,
width = 1.3,
fontcolor = darkslategray,
color = darkslategray,
nodesep = 1,
penwidth = 2]
Site [label = '@@5']
Depth [label = '@@6', color = SaddleBrown]
Burrow_Depth_Intrctn [label = '@@7', color = SaddleBrown]
# Endogenous Variables
node [shape = rectangle,
fixedsize = true,
width = 1.8,
color = steelblue,
fontcolor = darkslategray,
penwidth = 2]
Burrow_Density [label = '@@3']
Initial_SS [label = '@@4', color = darkslategray]
End_Mass_LB [label = '@@8', color = SaddleBrown]
# Soil Strength Interaction
node [shape = rectangle,
fixedsize = true,
width = 2,
height = 0.9,
color = steelblue,
fontcolor = darkslategray,
penwidth = 2]
CrabSoil_Intrctn [label = '@@2']
Crab_Density [label = '@@1']
# several 'edge' statements
#Soil Strength Exogenous Variables
edge [color = grey, arrowhead = normal, penwidth = 1, minlen = 3]
Initial_SS->Burrow_Density
Crab_Density->Burrow_Density [color = steelblue, arrowhead = normal, penwidth = 5, minlen = 4]
#All Endogenous Variables
edge [color = DimGray, arrowhead = normal, penwidth = 5, minlen = 5]
Site->Burrow_Density
Site->Initial_SS
Site -> End_Mass_LB [color = grey, arrowhead = normal, penwidth = 1, minlen = 3]
Depth -> End_Mass_LB [color = grey, arrowhead = normal, penwidth = 1, minlen = 3]
Initial_SS -> End_Mass_LB
Burrow_Depth_Intrctn -> End_Mass_LB [color = SaddleBrown]
Burrow_Density -> End_Mass_LB [color = grey, arrowhead = normal, penwidth = 1, minlen = 3]
edge [color = steelblue, arrowhead = normal, penwidth = 5, minlen = 4]
CrabSoil_Intrctn->Burrow_Density
}
[1]: 'Crab Density'
[2]: 'Crab Density and\\nInitial Soil Strength\\nInteraction\\n'
[3]: 'Burrow Density'
[4]: 'Initial Soil Strength'
[5]: 'Site'
[6]: 'Depth'
[7]: 'Burrow Density and\\nDepth Interaction\\n'
[8]: 'Final Litterbag Mass'
"
) ### Without Site
grViz("digraph Soil_Strength {
# a 'graph' statement
graph [overlap = false,
fontsize = 14]
# several 'node' statements
# Exogenous Variables
node [shape = rectangle,
fontname = Helvetica,
width = 1.3,
fontcolor = darkslategray,
color = darkslategray,
nodesep = 1,
penwidth = 2]
Depth [label = '@@5', color = SaddleBrown]
Burrow_Depth_Intrctn [label = '@@6', color = SaddleBrown]
# Endogenous Variables
node [shape = rectangle,
fixedsize = true,
width = 1.8,
color = steelblue,
fontcolor = darkslategray,
penwidth = 2]
Burrow_Density [label = '@@3']
Initial_SS [label = '@@4', color = darkslategray]
End_Mass_LB [label = '@@7', color = SaddleBrown]
# Soil Strength Interaction
node [shape = rectangle,
fixedsize = true,
width = 2,
height = 0.9,
color = steelblue,
fontcolor = darkslategray,
penwidth = 2]
CrabSoil_Intrctn [label = '@@2']
Crab_Density [label = '@@1']
# several 'edge' statements
#Soil Strength Exogenous Variables
edge [color = grey, arrowhead = normal, penwidth = 1, minlen = 3]
Initial_SS->Burrow_Density
Crab_Density->Burrow_Density [color = steelblue, arrowhead = normal, penwidth = 5, minlen = 4]
#All Endogenous Variables
edge [color = DimGray, arrowhead = normal, penwidth = 5, minlen = 5]
Depth -> End_Mass_LB [color = grey, arrowhead = normal, penwidth = 1, minlen = 3]
Initial_SS -> End_Mass_LB
Burrow_Depth_Intrctn -> End_Mass_LB [color = SaddleBrown]
Burrow_Density -> End_Mass_LB [color = grey, arrowhead = normal, penwidth = 1, minlen = 3]
edge [color = steelblue, arrowhead = normal, penwidth = 5, minlen = 4]
CrabSoil_Intrctn->Burrow_Density
}
[1]: 'Crab Density'
[2]: 'Crab Density and\\nInitial Soil Strength\\nInteraction\\n'
[3]: 'Burrow Density'
[4]: 'Initial Soil Strength'
[5]: 'Depth'
[6]: 'Burrow Density and\\nDepth Interaction\\n'
[7]: 'Final Litterbag Mass'
"
) New Decomp Visreg Plots
visreg::visreg2d(Decomp_lm_3,
"Depth",
"Post_Burrow_Count",
scale = "response",
main = "Decomposition Rate",
#breaks = c(0, 4, 8, 12, 16, 20),
xlab = "Depth",
ylab = "Burrow Density"
)
visreg::visreg(Decomp_lm_3,
"Post_Burrow_Count",
scale = "response",
by = c("Depth"),
#breaks = c(0, 4, 8, 12, 16, 20),
xlab = "Burrow Density",
ylab = "Litter Bag Mass"#,
#main = "2018"
#gg = TRUE
) #+
#theme_bw() #+
#aes(color = "Site")
visreg::visreg(Decomp_lm_3,
"Depth",
scale = "response",
by = c("Post_Burrow_Count"),
breaks = c(0, 10, 20, 30),
layout = c(4,1),
xlab = "Depth",
ylab = "Litter Bag Mass"
#main = "2018"
#gg = TRUE
) #+
#theme_bw() #+
#aes(color = "Site")Error Distributions
Tests for Normality and Non-Normality for Each Model Above
##
## Shapiro-Wilk normality test
##
## data: SS_Resid_2$resid
## W = 0.98425, p-value = 0.3064
##
## Shapiro-Wilk normality test
##
## data: Burrows_Resid_SS$resid
## W = 0.81721, p-value = 1.494e-09
##
## Goodness-of-fit test for poisson distribution
##
## X^2 df P(> X^2)
## Likelihood Ratio 591.5668 26 3.405385e-108## [1] 3.405385e-108## [1] 1##
## Test of fit for the Gamma distribution
##
## data: Burrow
## V = 0.18166, p-value = 0.8978
##
## Shapiro-Wilk normality test
##
## data: Burrows_Resid_PP$resid
## W = 0.81721, p-value = 1.494e-09
##
## Shapiro-Wilk normality test
##
## data: SD_Resid$resid
## W = 0.92669, p-value = 4.615e-05
##
## Shapiro-Wilk normality test
##
## data: SB_Resid_2$resid
## W = 0.83619, p-value = 6.37e-09
##
## Shapiro-Wilk normality test
##
## data: Decomp_Resid_2$resid
## W = 0.99213, p-value = 0.8931